For a generic use PC, you really don't need anything high-end. I'd probably be looking for a dual-core AMD processor system. I say AMD because for your purposes, the it's not worth paying the extra dollars for an Intel based system and you're not really going to notice the difference. Of course, if budget allows, by all means, go with Intel.
The system should have between 2GB and 4GB of RAM. 2GB is would be my minimum, but it wouldn't hurt to have 4GB installed.
As for hard drives, I'd recommend a system that has at least a 250GB hard drive. The system I'm typing on now has a 200GB hard drive installed (this is my general use PC). I just rebuilt this system about 6 months ago, and still have 148GB of 186GB of space available and I don't see a need to ever go with a larger hard drive on this system. For general usage, 250GB to 500GB is going to be plenty.