if you are talking about modern firearms, the list goes basically like this:
Every Navy officer and enlisted man qualifies on the C7A1 and the Inglis Hi-Power, though most people call it "the Browning". That is reality. The order of issue on vessels is a fair bit different though.
Generally, on ship, the main concern is boarding parties and "force protection" which if fancy talk for either guard duty or repelling boarders.
Generally, the C7 can be issued, but it is often more common to encounter the SigP225 if I recall these days. Boarding parties sometimes also get a variant of the C8 carbine. The Browning is more of an ARMY thing - the Navy guys usually get the SIG lately. They also issue the Remington 870P.
Submariners get issued the MP5(N) generally as it is compact for storage reasons, and it is also sometimes part of the Naval Boarding Party kit.