Well, *ahem* on behalf of the 1AT, I'm sure your more then welcome. We are a coalition of 7 SG's, one for blasters, scrappers, defenders, etc etc. We are very active, and are always looking for new people too come in and join the fun. We're mainly PvE, but we do also PvP occasionaly as well, so it sounds like we suit your playstyle. And also we do plenty of events, involving regular TF's and "Crazy Events" currently underway by Dolous. Also just recently had a RL meet up, which many of us found great fun.
If your interested, then feel free to sign up/browse our forums that can be found in my sig. Hopefully see you soon.
Jum 
Edited for spelling
The 1 AT or Last Line Of Defence are the two SG's I always recommend. Only because I stepped down as leader and left my SG when I moved over to CoV, otherwise the New Bloods would be the only choice ahead of those two rabbles
1 AT have a seperate SG/VG for each individual AT as well as a recently formed PvP group and are all in coalition with each other. A mix of players from newbs(NOT noobs), CoH guru's, PvP'ers and PvE'ers. Can get a bit rowdy and spamtastic on their forum but are very helpful and great fun to play with
Last Line Of Defence are a great bunch spanning three SG's and are one of the most laid back and friendly groups you'll come across. They have a VERY active global channel that is always full of banter and the one thing they do pride themselves on is making sure no one has to solo, regardless of level and will always leave teams and exemp down or alt to stop that and don't take themselves too seriously as the game is all about fun for them.
I can put you in touch with inviters from either of the two if you catch me in game on @kinslayer.
Sadly it seems as if my current Hero SG has all but died so am looking for a new home, so if theres any SG's out there currently recruiting and currently active, let me know, am a lvl 45 BS/regen scrapper btw, mainly into pve, but do a little bit of pvp from time to time.