Jonah's got a point. Dell computers have had a reputation of reliability.
I would recommend at least a 1.5Ghz processor (since so many people nowadays are putting up poorly-coded websites done entirely in flash), 256MB of RAM (512 if you're working with a lot of hi-quality pictures).
The digital cameras can be plugged into your computer several different ways. The most common are USB and Firewire. Firewire is also called IEEE-1394. USB is standard for every computer today, however firewire can be found on most of them as well.
There are two types of USB
USB 1.1 - runs very slow since it is the old USB technology
USB 2.0 - runs much faster, but USB 1.1 devices will still run at USB 1.1 speeds.
If you have a choice of how it will be connected, get Firewire.
Hope this doesn't confuse you too much. If it does, Photoread some back issues of "Maximum PC", that's where I learned a lot of my computer knowledge.