Among the new abilities my trooper got while leveling is a mortar volley which is surprisingly powerful. I didn't expect to be able to one-shot groups of 5 enemies in the final area of Ord Mantell. That somehow made up for the trooper getting his companion later than the other classes, which I wasn't too happy about. The smugglers that I shared the starting zone with all had companions for the final quests, while the troopers only get theirs right before leaving the planet, with no real opportunity of playing with them on the starting planet. Also I found the trooper's companion to be the least likable of all the companions I've seen so far, so up to now I'm underwhelmed by the companion feature for my trooper.
Next step in his adventures will be the first "flashpoint" or real group dungeon. I already did group missions with my guild on Ord Mantell, but on that planet the group missions are open world and not instanced like on Korriban. Having already played the Esseles flashpoint in the beta, I knew that it takes some time, so as it was getting late I rather saved this for the next play session. Instead I wandered around the Republic Fleet, learned my advanced class, talked with all the tradeskill trainers (each gives 450 xp), chose Bioanalysis, Biochem, and Diplomacy as tradeskills, and sent out my companion to gather the first components and craft the first medkit. I also looked at the Galactic Market AH, and found a cheap crafted blue item, as well as modifications for my new gun. I searched around endlessly for a modification station, until a guild mate told me that you don't need those any more and can just CTRL-click your weapon to modify it. Well, that explains why my trooper never got a quest explaining the modification stations, as my other classes got in the beta, although the mod station is still in Fort Garnik.