CPU and HDD access speeds, but mostly HDD. You can run a 8-player dedi on an 8GB system with a Linux server OS. I have done it on an old core 2 quad CPU with 8GB RAM and a SSD. It gets a little laggy if there are a lot of Z's in the hordes and you're in a large base with lots of electronics. It was playable though. I did it with the hordes spawn at 32 Z's, and max server Z's at 150 or 200.
Oh, and a good upload speed. I recommend having no less than 3MB upload for hosting a server. It's doable with only 1.5Mbps, but not enjoyable for players and they tend to de-sync a lot.