Well, any modern PC will come with 64bit Win7 (
which is nicer than Vista). I still prefer stuff with Intel processors in them. You can probably get a laptop with a quad core Core i7 processor in it for a pretty good price now but not the absolute newest generation i7 because you always pay way more for the newer ones and it won't be the lightest thing if you get a 17" model but I would say power is more important than portability in your case.
Get something with at least 6GB of ram. don't expect to use the onboard sound of course. I'm assuming you already have a USB audio interface.
Lots of expensive computers cost extra because of the video card. Since 3D/video isn't important for you don't need to pay extra for it. Unfortunately you have no choice with a laptop because you can't just omit the fancy video card and use something cheaper like you can when you build a desktop PC.
Something similar to this HP Pavilion dv7t Quad Edition series is plenty powerful enough for running Live.
http://www.shopping.hp.com/webapp/shopp ... tqe_series
Because every PC is slightly different and the hardware isn't made by the same company that makes the OS there can always be stuff that just doesn't work well with Live but things have been going pretty well since Widows 7 came out. It's works fine for me and many other people.