Six male and six female passengers and two children came on the Porpoise.
Mr. Commissary John Palmer and family (including son John junior b. 1797, two sisters, Sophia b.1777 and Sarah b.1774, and a naval brother, Christopher b.1767); Mr. E. Stamford and family; Mr. George Suttor and family; John Gearish, assistant to the gardener were mentioned in the Historical Records of Australia as passengers .
The Porpoise brought four tons of 1797 cartwheel pennies -
The Duke of Portland to Governor Hunter,
Whitehall, 12 April 1799
You will receive by the Porpoise near four tons of a new copper coinage of a penny each. The total value of the above coinage is £550 pounds, which you will take care to carry to the credit of Government, and to account for it in making such payments therewith for the public service as you shall from time to time judge most advisable. The circulation of this coinage must very much add to the comfort and convenience of individuals, and greatly facilitate their dealings with each other. It does not occur to me that there can be any inducement or motives of interest for sending this money out of the settlement; but if the contrary should be the case, it will be your duty to frame a suitable ordinance for preventing such an offence, subjecting all defaulters, as well the parties receiving as those disposing of them for exportation, to severe penalties. I am etcc., Portland. 
A 'cartwheel' copper coin made at Matthew Boulton's Soho Mint in 1797 - Perth Mint
A selection of useful European plants, arranged by Sir Joseph Banks, to replace those lost in HMS Guardian were also sent on the Porpoise.
Outfitting the Ship
The State Library of New South Wales in the Papers of Sir Joseph Banks has the following background note concerning the outfitting of the Porpoise for the voyage to New South Wales ......
'George Suttor, a free settler, was engaged as gardener on board HMS Porpoise in August 1798. In return for caring for the consignment of European plants to be transferred to the colony in New South Wales, Suttor received free passage to the colony for himself, his wife and their baby son, and the usual assistance given to free settlers.
Sir Joseph Banks, under instructions from the Lords Commissioners of the Treasury on 22 June 1798, arranged a selection of culinary and medicinal plants, fruit trees and vines, plants for fodder, trees for timber, hops for brewing and other plants which he considered useful or necessary to the colony. These were planted and cared for by Suttor in the Gardens at Kew before being received on board the Porpoise in October 1798. The ship had earlier been fitted with a plant cabin on the quarterdeck according to Banks' specifications.
Below is an extract of an Account by George Suttor of the voyage of the Porpoise from his Memoirs, by Walter E. Bethel, published in The Sun...... With his newly-wedded wife George Suttor set out on H.M.A.S. Porpoise to come to New South Wales in November 1798; but owing to a concatenation of circumstances they did not arrive until November, 1800. The voyage was impeded by many things and delayed through the war with France.
Son of a Scotsman, George Suttor was born in Chelsea, England. He grew up at a time England was at war with France. Everything was retarded by the war, and openings in life for young men were not plentiful. Officers were returning to England after service in New South Wales, and the tales they told of the vastness of Australia and its potentialities stirred the imagination.
In November, 1798, George Suttor left the Thames with his wife on H.M. ship Porpoise, and sailed for Portsmouth. They encountered heavy gales and nearly came to grief on Margate Sands, For a whole day and night they were in peril and lost two anchors. Eventually they arrived at Sheerness, where they remained fully two months. All shipping at that time was uncertain, in view of the war. The English Navy was actively engaged in keeping trade routes clear and bottling the French fleets up in their own ports. In January 1799, the Porpoise cleared from Portsmouth and reached the Downs in safety, and stayed there till the middle of February, 1799. Here she was commandeered by the Admiral to take some supernumerary seamen to Portsmouth and to convoy merchant ships to that port. This proved to be a long job - they were 30 days beating about the Isle of Wight, eventually reaching Spithead In safety.
By this time It had been established in the mind of the captain that the Porpoise was a very defective ship, and action was taken to dock her, with a view to the shortening of her masts and fixing of false beamings to her hull. For this purpose all the passengers had to be removed to another ship for the time being. In April, 1799, she was still at Spithead, and on May 1 1799, a boy was born to Mr. and Mrs. Suttor on board the Porpoise at Spithead.
Sailing was Indefinitely postponed, as the French fleet was reported to be out in the Channel. It was not till September, 1799, that they got away, and a noble sight that departure must have been, for there were fully 500 sailing vessels bound for all parts of the world, convoyed by H.M.S. Lancaster and 20 ships of war. The French fleets had been 'bottled' in their ports for the time being.
About a week out on the voyage a great gale sprang up. Three men-of- war went down; on one were the Duke of Kent's carriage and horses, and those on the Porpoise saw the drowned horses being swept past their vessel. The rudder of the Porpoise was broken, and she was ordered hack to England, arriving at Spithead in about eight days. Here the Suttors, full of a distrust of the ship, made up their minds that they would no longer sail in her. 
The authorities later on decided to cancel her voyage and selected another ship, a fine Spanish corvette - a war prize - called the Infanta. Her name was changed to the Porpoise, and on March 17, 1800 (St. Patrick's Day), the Suttors again put to sea, and all went well on this new voyage. 
They reached Capetown on May 24, 1800. Nine prisoners, all former soldiers, were embarked at the Cape of Good Hope
Convicts of the Porpoise identified in the Hunter Valley:
Johannes Gysbertus Pellikorn
The Porpoise remained at Capetown for four months, sailing eventually for Sydney on September 13, 1800, and reaching the Heads on November 8, 1800.
The Porpoise arrived in Port Jackson on 9th November 1800
The Suttors' impressions of Sydney as it first met their gaze furnish most interesting pictures of those early times. Sydney Cove was a quiet, secluded bay, resembling the many others on either side of it. On its placid bosom were a few sloops, a few boats, a convict ship from Ireland, and two small wharves, one on each side of the cove. One was called the King's Wharf; the other the Government Wharf. Campbell's Wharf was in course of erection. The town of Sydney itself presented a very unfinished, crude appearance, more like a camp than a town. Stumps and dead trees abounded everywhere. A large part of the rapidly-formed town was given up to the New South Wales Corps, who were living in huts, and other homes were constructed of wattle and plaster, with thatched roofs - white washed Inside and out, some with windows, most of them without.
Where Pitt-street now runs were a few weatherboard shops, as there were in the thoroughfare now George street. Old Government House, in its early size, picturesque and comparatively stately, gave promise of better things to come. Near at hand were the small Barracks and a dirty old gaol; close by was the male orphan school, while on the waterfront was a small dock yard, with a couple of vessels building. This was the Sydney that greeted the Suttors in 1800, and it is safe to say that this, devoted young couple, thinking of the comforts and refined conditions of old Chelsea, must have had many misgivings, and felt in their minds that it seemed a poor prospect after such a long and weary journey. ' 
Then came Suttor's Interview with Governor King, and having come straight from the suavities of courtly old Sir Joseph Banks the downright- ness of his Excellency somewhat puzzled the young pioneer. King had just assumed Vice-Regal office and was probably finding his job not a bed of roses. He apparently was not inclined to draw roseate pictures for newcomers. In his memoirs Suttor remarks that Governor King was sometimes the gentleman sailor that he was; at others, well, very rugged. 'He told me,' said Suttor, 'to look on every man in Sydney as a rogue and not to trust anybody. Further, that he could not be troubled with my affairs, as he had 6000 to govern, which was all that he could do.'
For two weeks the Suttors, acting on the Governor's advice, stuck to their old sea home, the Porpoise. She was lying close to the shore, Suttor explained, and one could go ashore frequently. Just as we nowadays take dives from the many silvery beaches of Port Jackson, so Suttor tells us, he took his dip in Sydney Cove.
At Parramatta, Suttor met his friend George Caley, who was stationed there as a botanical expert. 
In HRA there is a list of 28 men belonging to H.M. Porpoise who wished to be discharged from the Service to remain in the Colony
Charles Griffin - ship carpenter, later master boat builder
Departure from the Colony
After various Colonial duties the Porpoise set sail for India in 1803 under the command of Lieutenant Robert Fowler and in the company of the Cato, Captain John Park, and the East Indiaman Bridgewater, Captain Palmer.
Captain Matthew Flinders famous as the first known person to sail around Australia, confirming it as a continent, sailed on the Porpoise as a passenger.
The Porpoise and Cato were both wrecked on a coral reef 729 miles north of Port Jackson on 17th August 1803.
Wreck of the Porpoise (image)- William Westall - National Library of Australia
Select here to read an account of the wreck in the Historical Records of Australia written by Lieutenant Fowler, Commander of the Porpoise and entrusted to Matthew Flinders when he set out in a small cutter for a 1000km voyage to Sydney to arrange for the rescue of crew members.
Notes and Links
1). The Naval Gazette.... Porpoise (A.S.) (S). Lieut. Fowler, 12, T. 1795; lost on a coral reef off New South Wales in lat22 deg. 20min. S. long. 155 deg. 52. E., August 17, 1803. Crew Saved.
2). PALMER, John. Commissary, magistrate and landholder Came free as Purser of the 'Sirius' on the First Fleet in 1788 and on 2 June 1791 was appointed Commissary; in September 1796 he left for England per 'Britannia', returning in November 1800 per 'Porpoise'; he went to England with Bligh as a witness in 1810, and was demoted to Assistant Commissary in 1811; in June 1813 he was reemployed in the Commissariat and returned to New South Wales in May the following year; he was granted land in the Land District of Bathurst, County Cumberland in 1818 and in January 1819 retired on half pay. He was a member of the Committee of the Female Orphan Institution from August 1803 to January 1824 and a magistrate. Colonial Secretary's Index Biography
3). SUTTOR, George (Senior). Superintendent of the Lunatic Asylum at Castle Hill Came free per 'Porpoise', November 1800 in charge of plants sent to the Colony by Joseph Banks; land grant at Baulkham Hills; accompanied Bligh to England in the 'Hindostan', 1810, returning per 'Mary' in 1812; appointed Superintendent of the Lunatic Asylum, Castle Hill. Colonial Secretary's Index Biography
4). MCKABE, Matthew. Per 'Porpoise', 1800; of Hawkesbury 1820 Came from the 6th Regiment at the Cape of Good Hope to join the 102nd Regiment here. For permission to remain in Colony (Fiche 3203; 4/1861 p.31)
5). Sir Joseph Banks put forward Mungo Park to undertake explorations in Australia. He was supposed to have sailed on the Porpoise however this did not eventuate. From Historical Records of Australia.......' Mungo Park was born on the 10th of September, 1771, at Fowlshiels. He was educated as a surgeon, and obtained his diploma at Edinburgh in 1790. In May, 1794, through the influence of Sir Joseph Banks, he obtained an appointment as an explorer to attempt the discovery of the source of the Niger on behalf of the African Association, a corporation founded in 1788 for African exploration. In December, 1795, he set out from a point 200 miles up the Gambia, accompanied by a negro servant and one boy with one horse and two asses. Six months later he returned after having reached Sego on the Niger Eiver. When a survey of Australia was under consideration in 1798, he was offered the charge of the expeditions at a salary of 10s. per diem, but the negotiations failed. In 1805, Park set out on a second expedition to explore the Niger, during which he lost his life.
6). Matthew Flinders reached Australia on 28 January 1802 in the Investigator and later explored what is now known as Queensland in July. He continued his expedition of Australia until June 1803 when he was forced to abandon the Investigator at Port Jackson in NSW after the ship had rotted from a leak.' Captain Flinders attempted to return to England later in 1803, in command of HMS Cumberland, however was imprisoned at Mauritius for six years. He died at age 40 on July 18, 1814. He was buried in St. James Church, London. In 2019 his grave was discovered by archeologists among 40,000 other human graves expected to be dug up ahead of the development of London's new high-speed rail network.