Loreen,
I'm not going to mince words here. If you want to pay $60, go with a reputable company that provides you a VPS for that price. Your likelihood of getting a good product and service is very good then.
If you go with someone trying to peddle a dedicated server for that price, you're going to either end up with ancient hardware that will die at any moment, abysmal support, oversold bandwidth, etc.
The simple fact of the matter is that one cannot profitably sell a $60 dedicated server without cutting corners on you.
The closest thing possible would be to sell you an Atom dedicated server in a chassis that allows two of them per 1u of rack space. Even then, they would be foolish to charge $60, because the margins are still not conducive to a good business model.
The point here is, don't just think with your wallet, because if you do you'll end up fucked in the end, one way or another. Find the right balance of price, quality and reputation. Good luck!
P.S. To any hosts on here offering dedicated servers for that price point - this is not a jab at anyone, I'm merely calling it as I see it.