I've got an HP laptop that I bought with tax rebate money almost three years ago for ~$1,000, with an AMD dual core Turion, and it's been flawless except for the battery going to shit since I always leave it plugged in and on. I NEVER shut it off unless I'm taking it somewhere, and I use it every day, and it works great. It plays DOOM 3 like a champ, so as far as I'm concerned its way more powerful than it needs to be. When I first got it, it had Vista on it and after a short while starting running REALLY hot. I eventually installed Win7 and now it runs nice and cool.
If you aren't gaming it, and you aren't, then don't worry about having the fastest processor, a 2.0+ dual core should be a minimum but will do you fine. Worry about the quality of the rest of the thing. HP/Compaq make very nice laptops, start there, and don't worry so much about who makes the processor so long as whatever you demo runs fast enough for your liking, which should be anything in the store, even the little Atoms.