Swiftsure is an amazing server for Republic PvP. Roll on it. It's the highest population server in the US, if not the world, meaning it's active 24/7. PvP is always going on.
The Swiftsure also has queues 24/7 so I would NOT recommend rolling on that realm. I'd actually recommend rolling on any other realm.
My realm, West Coast PVP Shadow Town has a pretty sizeable Republic side community and my guild currently has multiple groups running PVP all the time. Come check it out, my character's name is Ganoes if you give the realm a shot.
The swiftsure does not have queues 24/7. The only time Swiftsure has queues is on Saturdays and Sundays, and even then it's just 30 minutes at most. Don't listen to someone who doesn't play on the realm
Recommending people to roll on the highest pop realm at the exclusion of other realms that need more players is honestly pathetic. Don't do that. And stop lying. I have tried the realm and it does have queues 24 / 7.
I'm not lying. Log on right now. There are never queues on the weekdays. Maybe you tried rolling on it at launch, and that would haev been true, but now, no.
And besides, I'm just answering the OPs question in the best way I can - Swiftsure is a great PvP Republic realm. If that offends you in any way, I apologize.
http://i.imgur.com/0K8XN.jpg <-- screenshot of me right now, battle waiting to ensue. Just to show the OP what the activity is like.
My main is on swiftsure empire side, no the que is not even close to 24/7, for a several hours a day there is one but dont exaggerate without the facts.
Another server to try is The Crucible Pits (PST), quite a few PvP guilds from other games (WoW, Warhammer, etc) came here, and PvP is pretty common and the main focus of pretty much every guild here.
The Republic are outnumbered are 2 to 1 but we're doing fine and usually win fights.
P.S. The server population is pretty large, it's usually listed at heavy and very heavy during the weekends.