Hi Tom and welcome to the forums!
First of all, if I'm not confused I think the D7000 will be out of your budget so we can get it out the way already. So now we are with the 650D vs D5100 vs 600D. I would recommend you to read Gordon's reviews of the D5100
. Also if you want you can check Gordon's D7000
I think you should note that touch screens really don't tend to fail, I've owned several products with touch screens from different brands and I've never had any issues of malfunctioning. So if the touch screen failing is your only concern - which I think you shouldn't worry about - I can tell you that the 650D has quite some more advantages over the 600D so for the moment I will get the 600D out of the way.
Now we have D5100 vs 650D. At this point I think it depends a lot on what are you planning to shoot.
So my questions here are: What are you going to use your DSLR for? Have you owned a DSLR before?
And by the way, the lens is the most important aspect to take a picture but the camera body also comes into play and in the film-era it might have not mattered that much, but now the camera is like the film as well so you have to choose wisely.