Question about backing up games

[Groo The Perverted]

I'm getting a PS3 Slim this coming Friday, and I had a few questions about backing the information up.

Trophies are connected to PSN Name so that's not to worry about.

But I can't copy the GAME DATA.

I can copy the saved data, which I've backed up individually to my external HD (saves it in a folder labeled PS3).

Is that enough? I mean....I started over before, and lost all the online challenges I did on Burnout Paradise.

I don't want to have to do that again. I thought that was tied in to something online, not my personal save information, but I was wrong.

So if I back up all the saved data that I can (some games won't let me) will that be sufficient?

Then I connect the external HD to my new PS3 Slim and ....what? restore data?

I've never had to do this before so sorry for dumb questions but I'm wanting to make I don't screw this up.

I was thinking I had to copy the gamedata too but apparantly I can't.