Don't forget a proper choice of control panel (or none, works best ). DirectAdmin, from my experience, is better compared to a more bloated cp, such as cPanel, Plesk, etc. RAM is probably an equally important factor, especially if you choose a VPS, since you need to make sure you get a minimum guaranteed amount to be able to run your site smoothly.
Well as you are saying a DEDI for a Proxy...that means that you are getting some serious traffic and as per your previous post in anohter topic about cpu limit..that would only mean that you are getting huge traffic aand need a better solution so this is what i would prefer.
This is considering the fact that your current host is on a high end server.
So you would need something like:
P4 3.0ghz w HT
1.5-2gb ram
40gb-80gb hd (any smallest)
10mbit unmetered
Cpanel
Pro-Active Management
You should look into high end servers if your proxy is really resource intensive.
Bandwidth ofcourse and a webhost that allows proxy websites. CPU utilisation is none for a proxy server. RAM should be 1GB+ for a good proxy with nice number of connections at a given time.