Welcome to the forums! We Are an International Fleet
Red Squadrons would seem to fit your criteria well, we do have a laugh (even if sometimes its over something silly ^^) we do support players wanting end game PvP and PvE and RP, and with 11 years of experience, I think we're a pretty bonded fleet
We are a military styled fleet, with the Red Squadrons Taskforce serving as our Federation Fleet and the Red Squadrons Battlefleet serving for our Klingon players! And if you want to play in both, your more than welcome (we do encourage it to develop PvP tactics .
We're pretty well known around the Trek gaming community and know a lot of cool fleets whom we have a laugh with pretty often!