Jeremy,
I used to run a
network that had 5 web servers each dedicated to its own site. This was way overkill for the web traffic. The servers took a lot of hits. It ws the database backend servers that took the load. Is your new site DB driven with a lot of transactions? A regular REDUNDANT server would be just fine for a regular site that takes a lot of traffic. It's what happens when you have DB's and such. I run a web server out of my house that could probably handle your site

, however you need redundancy drives, power, etc... I've used both Verio and Rack space before, but can't really help you from there since it's been a long time.
Ritch