It doesn't take much. The most important factor will really be your internet upload speed.
Any modern dual/quad core CPU, 2GB+ ram, any regular internal HD. You may be able to run it on the existing parts you have.
Get a cheap 1155 i3, 4GB ram (ram is cheap), and a nice 7200RPM internal HDD and you will be set.
My current setup still needs a Hard Drive (fried the other one uninstalling Ubuntu). It has 1 gig of ram (it was like 3-4 years ago I got it) so I will def. need to upgrade that. It came with 1GB ram (2 512 sticks), and like a 200GB Hard Drive.
I will for sure upgrade the ram to around 4 Gigs, and a new Hard Drive. I am thinking of running it as a Linux-based server. I don't know what the common linux distro is for a dedicated server, I'm more used to Ubuntu, Gentoo, and Fedora though.
I think (from what i've seen) that 512 is supposed to support 10 players (vanilla, no mods), so 4GB should be able to handle 20-30 players with Craftbukkit, I'm thinking.