Dropped mine on my tile floor recently; the floor won. Lots of good advice here and many options. But what brands, etc. should I stay away from?
Gateway is the devil. I seriously had one that didn't function properly from day 1, and the lady at BestBuy claimed I was making things up. Not a happy experience.
HP is ok, but overpriced for what you get. Not worth it.
Acer has a good reputation, but as I said, I've known a lot of people with bad experiences, so I wouldn't personally go with them.
I would personally go with: Asus, Lenovo, and mayyyybe Samsung and Sony. I have no personal experience with the last two, but a number of techie friends have recommended them.
As far as processors, I pretty much limited myself to the Intel Core i5 or i7, but I want to run a pretty hefty GIS program. I wouldn't go below 1.5Ghz if I could help it, and either 7200rpm, or 5400rpm combined with an SSD, for startup speed.
4gb of RAM is plenty to run most programs, and upgrading ram is EXTREMELY simple in most computers, (Lenovo u410 excepted, since it's trying to be a Mac), so I definitely wouldn't spend a lot of extra money worrying about the RAM. If it drives you nuts you can always add more later yourself, fairly cheaply.