I would say 6D and 24-105. I'd also say a tripod is useful but not 100% necessary these days. With the 6D you'll be able to get great shots at ISOs the 600D would cringe at. Add to that 3/4 stops of IS and, really, do you need a tripod? I have one but it rarely gets used (mostly because its big and heavy).
Nothing wrong with the 17-55 though it's an EF-S lens and that limits you to crop bodies. Shame cos it's a really nice lens. Even then you get shallower dof with the 24-105 on the 6D. I think the 6D is a bargain, I kinda wish I had waited and bought it instead of the 5D II just for that high ISO ability.
You could look into a second hand 5D II as a cheap alternative. In terms of IQ it's still one of the best out there.
Tripod use depends entirely on how long your shutter speed needs to be. For long exposures, of course, you will need a tripod. It doesn't matter how high you can push your ISO. E.g., as Neuro said, architecture photography to get rid of those extra people, star trails, night photography where you want to record light trails. That said, yes, you're right, you can't go wrong between a 5D2 and 6D but for a little bit extra, 6D is worth every cents.
Yeah, depends on OPs style of shooting. I doubt as a newbie he would be out doing star trails etc with a 600D and 18-55. my point is for all general purposes you can manage without a tripod. It is only really specialized use like you said long shutter speeds where you will undeniably need a tripod. Therefore a 6D and 24-105 covers the widest range of applications.