The Maltese actually worked like this :
A Knight/Noble finances a ship - He hires workers and soldiers - he sends them to raid muslim ships under the command of one of his(The knight/noble's) friends(usually a skilled seafearer) The Knight/Noble gets about 50% of the booty and Workers and Ship Crew get the other 50%(or the Knight gets 75% and the Crew 25%)...so it was really a hiring job more than a permanent one...but it could make you rich for life
I have a Ship in a Bottle of one of the ships that the order came to Malta in from Sicily(they had three Grand Carracks - Remember MTW2?)
It's name was the Sant' Anna(Saint Anne)
The Order usually named it's ships for Past Grand Masters (La Vallette, Cassiere, L'Isle Adam, La Sengle) and Saints(Saint John, Saint Paul, Saint Anne, Saint Joseph etc)
Most Maltese Towns have their name after Grandmasters(Valletta, Senglea(Isla), Citta Pinto(Hal-Qormi), Citta Rohan(Haz-Zebbug),Citta Vittoriosa(Birgu), Wignacourt Street etc) - This was just trivia
The order had limited ships, the rest were owned by Nobles
Number of Galleons :
1530 - 3
1562 - 6
1590 - 3
1674 - 7
1686 - 8
Middle 18th Century - 4 Sailing vessels, 4 Galleys, 4 Frigates
Head of Order's fleet = Admiral - Head of the Langue of Italy
Naval Commanders = Captain General of Galleys - Elected by Grand Master and Council
Captain of Galleys - Also Elected
Crew = Galley : Knights & Servants at Arms, Soldiers, Sailors, Tradesmen, Pilot & his assistant, doctor and Captain
1670 - Flagship(Capitana) - 220 Members, Other Galleys - 181
The Grand Harbour was the Main Harbour, and Birgu(Ctitta Vittoriosa) was the Official Harbour(docking, loading and stuff)
Here is the best article on the navy(pics included at bottom of article, above references :
http://www.geocities.com/melitahistoricac/hw19946.html