Issues when buying used games? (simple question)

Hello,

 I’m just wondering something about buying used games:

I never really used PS-games online, I only had a PS2 before but never even connected it to the network.

So now I do have the PS3 connected obviously and do plan to use more online-features for current games.

But, when I’d buy games used, would there be any "problems" with it when someone else already used it online before?

Like perhaps that their results/achievements/etc. and what not are connected to that disc.

Or is it all just per online account, so if I’d use mine on my system, everything is starting at 0 again?

Or maybe even like "This disc has already been registered (or whatever) online before.".

It’s just I’m not sure how it works.

I don’t want to be buying a used game and then everything online is already done or something. XD

Well, I guess it’s not that way, would be annoying, but just making sure.

Greetings.