Hear me out a second. Now I know what I'm about but say isn't an FPS but you should really consider (if you haven't got it already) The Last of Us. The story is beautiful and the fractions mode is pretty intense.
Other than that I suggest Fallout 3 and Fallout New Vegas. No online however they're so damn big, you don't need an online mode. Exceptionally fun too!
If you want a multiplayer FPS, Rainbow Six was good.
No. Sniper Ghost Warrior is the most massive pile of wank ever.
I think you ought to just bin your old console, and buy a newer one.
The online community of all the fps games on the PS3 is dead. Battlefield 3 and 4 and the most recent 2 or 3 CoD titles are going to be the only things with anyone playing them, so if you want multiplayer, those are your options.
If you want single player, then there's a lot more choice, but single player is lame, it's...
I'd recommend Metal Gear Solid 4 as it takes about 15 hours to play through the story if you do it right and don't just speed play it. But if you've not played the previous games you'll have no idea what's going on.
I'd recommend getting a steam account and buying games through that. They're dirt cheap on steam, the summer sales are legendary on steam and there's a lot of free to play games.
Ignore me, SE:V2 and 3 were both so similar that in my head I'd merged them into the same game and thought that both of them were V2... I miss the original, I wish they'd just remastered it and kept it all exactly the same.