Do you play intensive games (Doom 3, Half Life 2, that kind of thing)?
If yes, reply back.
If no, then the specs don't matter all that much (mostly..)
RAM: minimum 1GB, ideally 2GB. All computers today should be sold with 1GB minimum anyway.
Processor: Ideally a Core 2 Duo or other 'dual core' processor. But most will do.
Hard drive: this is the thing you use to store all your photos, documents, programs, everything. You want this to be as large as possible. 250GB, or as large as you can find. You won't think you will ever fill it, but you will.
Also: once you settle on a computer and buy it, see how much hard drive space there is. Then go and buy an external hard drive with more space than that one (again, as large as you can afford). Use this for backups (there are free programs on the internet to do this). With this much information stored, you don't want to lose it! (And hard drives are mechanical and can lose data at any moment, but usually last a good few years).
Also -- it may be hard, but if possible go for Windows XP and not Vista. You'll have less hassle and the system will run faster.
(Side note: depending on how much you're willing to spend, take a good look at Apple Macs. They more stable than Windows systems, and every one is built to be able to do anything with it, so specs are less of an issue.)