From my sig: Pick two: Cheap, reliable, space/bandwidth.
You mentioned all three, but limit it to $60/month.
What do you plan on using it for? What's the budget like? $60/month max? Are you sure you need a dedicated server and not just a web hosting account? Will you be managing the server on your own and if not, have you planned for this already? Any idea on how you'll be backing things up? Does that $60 need to include a control panel? Fantastico?
Define your needs, and then it'll be much easier to figure this out.
1. Define your needs
2. Make a list of 10 companies that can provide your needs
3. Contact each one and see how they respond
4. Based on what you get, rank them in a list
5. Narrow it down to 3-4 providers
6. Figure out what will determine who you go with and contact each with follow up questions
7. Get it to a point where you've found multiple hosts that all fit your criteria and then see where you get the best price. Notice pricing was the last part - if you're doing something other than a personal website, it's usually seen that the revenue from a site will cover the necessary costs, or the needs of a business will justify whatever the price is.