Eclipse is a bit of a memory hog, so I'd recommend something with at least 2GB of RAM. More is always better.
My laptop (IBM ThinkPad z60m, running Linux) struggled until I added more memory. I now have 2GB. It can still take a few minutes to start up Eclipse, and several minutes to start up the Android emulator.
I use Eclipse at work on a Windows laptop with 2.5GB RAM, and I have to be patient. Once Eclipse has started, and you've opened a few files then performance is OK.
You don't have to have the latest top of the range PC. I'd imagine most recent PCs will be OK. Just make sure you're not limited to a small amount of RAM.
Mark