Hyperion used Dedicated servers for most of the time we ran it, however, we started out using a VDS and upgraded it as we went.
Our original host was

These guys have really high connection speeds and high quality servers, but they're REALLY expensive.
We then switched to a very cheap alternative with

These guys are dirt cheap, but you get what you pay for. The servers have the lowest connection speeds I've ever seen and really bad service. When we were getting DDoSed, you can blame these guys pretty much.
Then lastly, we switched to my personal favorite host we ever had,

These guys have lots of servers and options, decent customer support. They aren't my favorite for reasons of quality or service, that would be NFO, but they are my favorite because they are still pretty cheap.
One other option I advise people to look into is

They are really cheap, and they get all of their servers through OVH so if you can go without the services OVH offer and half the connection speeds, you can go with them instead and save yourself a LOT of money.