Well.. PVP is your best bet, ship combat especially in T1 as we have a nice advantage with the starting equipment. PUG's are fine (ship combat wise).
If you have spec'd into mostly ground traits then ground combat is a hell of a lot of fun.. Hell, ground combat is a hell of a lot of fun regardless.. (im biased, n have been lucky with my pug's)
With pvp medals you can get some nice loot (pvp medal rewards are found in Ganalda system in Eta Eridani). You don't need any of that loot tho as the gear you start with is better than most u find. I sold most of my pve/pvp medal gear anyway.
If your more pve focus'd, your in for a rather boring time as only Kahless missions and (single ground/space missions like Fed ver of Starbase 24 are available). Sorry can't remember there name.
You will get plenty of missions from the guys in Q'ono's but the majority are all pvp. There are the occasional mission like the kill XX npc ships, but they are the exception not the rule. Most of the missions available are "do x/x hostile engagements or house battles" or Kill x klingon captians or Fed captians.
That being said, the pvp is still fun and you will get in match's really quickly as there are alot more feds in the queues than Klinks.
deepinding on your play style and what you find entertaing
unlike fed its interily possible to almost never do ground(or vise versa space) anything
i persoanly find ground combat mindnuming so unlike fed i never have to do any ground missions so i speced my toon and skills for space and enjoy playing that way
and as far as space goes you basicaly have 2 choices bop or cruiser (raptors more or less usless)
so id recoemnd either a sci or tactical captin if your going to play bop thru teir 5 and an engineering captain if your going to fly cruisersd once you get to teir 3
the bop makes a nice dmg boat if you got with a tactical build but its alot squishier then fed escorts where it really comes into its own is as a sci ship as unlike fed sci ships you get the tactical initave and thus can use your crowd control ablitys more effectivly at the start of a battle
then theres the cruiser which if you go engy captin can have a massive tank if set up right at any teir i can tank any fed indefently and 2 or more feds can kill you if your by yourself but it takes em a while
in teir 1 and teir 2 your primary pvp stratgey will be hit and run as kligons only have escorts in those teirs
int3 and on deepending on you teams ship mix you can continue the hit and runs or if you have 3 cruiser that are healing eachother you can go for a more slug fest staregy as 3 properly set up cruisers working togther are almost impossible to kill while simultaniously trying to keep the bops alive and kill the feds
Savaage makes some gr8 points.. I shoulda pointed out that I have 3 science toons (1 ground spec'd and 2 space) 1 engineer (ground) 1 tactical (space). Now that you have the ability to make Klingon toons.. you can swap n change, try out different race's, try out space n ground.
I've played ground with my space toons and hated every minute of it.. but playing with a ground science guy for example.. LOVE IT. Ground captians are not gimped quite as much in space, as Space captians are gimped on ground pvp.
Check out the posts by Meat_Machine. He knows a hell of a lot about Klinks.