I'm still quite new to the beta, but I thought the same thing you did...that is, get the lightning and go exploring. That's pretty much what I've done. I haven't bothered with squads or group play yet, as I'm still just getting the feel of the game. But I went out for the first time last night to try and find some action.
I ended up on Esamir (just took the first warp I could find). I play NC, and we had some bases there, along with the VS. I traveled south looking for someone to attack. Then I came across my first enemy...an infantry in an ANT and another infantry on foot. Both were quickly dispatched. After that it was an infantry and a MAX of some sort. I'm assuming AV because he started kicking my ass...had to run away like a little girl.
Went to our station and got a new lightning (I don't have repair yet) and went back, this time it was 2 reavers and a skeeter. I don't think the reavers saw me, or they must have been newbs like me, because they never attacked. But that skeeter did...he didn't like me shooting him with my chaingun. We dueled with each other for about 30 seconds...I was down to about 1/3 health, but I think I got him pretty good when I went link dead. Was late by that time, so I went to bed.
All in all, it's a lot of fun so far...I wish the effects were a little better, but my graphics detail is down pretty low. I would really like to find a couple more lightnings to do some hunting with...maybe tonight...
-shark