I would suggest getting a decent vps, it would out perform a low end dedicated server, for $50 your not going to get much but desktop hardware, or Pentium 3/4 hardware and you can't expect much just to run a 1u server or alike your looking at $50/m with only like 1TB in bandwidth, hard to make a profit.
Take a look at the costs.
Co-location costs
Space $20-25
Bandwidth $10-30 a month
Power $10-20 a month
That's not including insurance, support, or anything related to the server.
Your looking at $40-100+ depending, where, what type of data center, what country, bandwidth, and power costs, It's hard to get 1 server lower then $30 a month unless you got a lot of servers and your getting good pricing.
At $50 that would be 15 minutes at most places in remote hands alone.
Why not increase your budget to $100 then get something decent within the past year.