I think to play online, you just need an internet connection (a good one for less lag/delay) and then you can just make an acc and connect, since PSN is free.

As for the team deathmatch stuff... Idk. I hate CoD.

While I have a PS3, I hardly play online with it, let alone Black Ops. I would assume a lot of the features your looking for would work the same way as they do on the 360.

I'm sure there is a system link option for playing offline, and as far as custom playlists and in game match option, If it is available in the 360 version, you would probably go about doing it the same way on the PS3.

As far as i know, they only real feature the PS3 lacks when it comes to online play in comparison to the 360, is the lack of a party chat and I'm not sure if in in game chat works the same way as the 360.

Just screwed it and got a PSN account by connecting my Ethernet cable to my system. The switching back and forth gets annoying, but now I get Black Ops and MW3 online, along with any other games I buy in the future.

if you're thinking about getting a new game, I recommend getting a PS+ subscription instead, it's $50 for a year and there's a rotating list of games you can play as long as the subscription is up. If a game leaves the rotation, you can still play if you got it before it was cycled out, it still counts as purchased on your account (unless the sub goes away of course)

Basically you'd get more games for less money in the end.