@Hollyh: More than likely, you'll buy a computer with the Windows Vista operating system - there are several 'flavors' of Vista and you will probably get one with the Home Edition; that is all that you need.
However, with Vista, you MUST get at least 2 GB of RAM for it to run satisfactorily - Vista will run with 1 GB but will be very slow. Likewise, for Vista, I would get a CPU that is 'dual core' and has a speed of 2 gHz or more. @Carbondudeoxide is right that you don't
need a dual core for your intended purposes, but time marches on, and you've already shown that you'll probably keep this computer for awhile - you probably won't find a 'single core' processor, anyway!
The other processor choice you'll have is: AMD or Intel - it doesn't make any difference (as long as the speed and number of cores are the same); AMD based computers are quite often less expensive than Intel.
I don't know if you belong to Sam's Club or COSTCO but, quite often, they have computers that would serve you well and may extend the factory warranty. Be careful in other stores to buy only what you want and need - the salespeople can be quite testy!
Best of luck with your decision.
EDIT: This was written before your reply, Hollyh, and before Saviour's. I would disagree with Saviour regarding Vista/XP for you and recommend Vista Home Premium. With your propensity for keeping a computer, there is no need to buy one with 'yesterday's' operating system. Except for 'power users' and 'gamers' the complaints about Vista are mostly past tense. You will also find a much larger selection among machines with Vista installed.
Just my opinion!