The service record shows that he joined the Navy in May 1906, the engagement being for 12 years (that was obviously extended by WW1) - the stuff at the top shows his personal details which I think are straightforward
He initially joined HMS Nelson - at this time it was an old ship (built 1876) that was at Portsmouth, and employed as a Training Ship for Stokers - he then briefly moved on to HMS Victory: this refers to the Naval Barracks at Portsmouth. I note a short period on the Hecla - another old ship, which in 1907 was at Chatham as a Depot Ship.
His first seagoing ship was the battleship King Edward VII. Note that his rating moves from Stoker 2nd Class to Stoker 1st Class and in 1910 he is an Acting Leading Stoker. The last column is for 'character'; he starts off as 'VG' (very good) but moves to 'Supr' (Superior). Note the 'badges' column which records the awarding of Good Conduct Badges (chevrons) which were awarded in 1909 and 1914.
In 1910 he is back on shore in barracks at Portsmouth (Victory) before spending a short period with HMS Fisgard: this was another training ship, for mechanics and artificers, at Portsmouth. He probably did some more training, as he is noted as being an Acting Stoker Petty Officer after this.
In 1911 he goes back to sea, this time onboard the cruiser HMS Hampshire.
A brief period on the old cruiser Flora, then to shore barracks at Chatham (HMS Pembroke) and Portsmouth (Victory and Vernon) before a short period on the cruiser Liverpool and then in August 1915 he joins the cruiser HMS Birkenhead, which he serves on through WW1, being discharged in April 1919.
I will try and find out a little more about the movements of KEVII - Hampshire - Liverpool - Birkenhead and get back to you.
Re: Coquette: was a destroyer, and in records of the time it was normal for all the accounting/paperwork etc to be done on a larger, parent ship. I would suspect that during one of the spells shown on his record as being in barracks, he was with the Coquette.