A question I would ask is, how you plan to finance the purchase. You may not be aware, but in few circumstances can you get a loan under $50,000. When you do find it, the rates are usually pretty steep, unless it's offered through Fannie Mae or Freddie Mac.
Are you planning to pay cash? For homes meeting your criteria above for the price you're willing to pay, there is usually much work involved. You can have repair costs rolled into the loan amount which would boost the loan amount.
Let's talk privately, so I can get more information to guide you through the process to acquire your home..
Short Sale & Foreclosure Resource