Rosebud, I wouldn't go for a laptop unless you're going to be using it at places other then your home. Laptops are a lot more expensive (really good ones anyways) I go to University and use the PC's there and can even access my home PC using Gotomypc software...Anyhow...Look for Intel Pentium Processors, AMD's are pretty good too. Stay away from anything that says Celeron, they are cheaper but also run half the speed of Pentiums..
In terms of memory, you want at least 512mb, recommended is 1GB and see how much it is expandable, usually anywhere 4-6GB. Processor speed, mine is at 2.66Ghz, tops are around 3.4Ghz so anything close to 3.0Ghz is more than enough.
Here is a breakdown:
Intel Pentium Processor 2.5 to 3.4 Ghz (anywhere in that range)
512MB of RAM (memory) (recommend 1GB)
ATI or similar 128 MB DDR or better (Video Card)
80GB or better Hard Drive (Reccommend 120 GB)
-to be nobody but yourself in a world which is doing its best, night and day, to make you everybody else means to fight the hardest battle which any human being can fight; and never stop fighting.- e.e.cummings