I would say that finding a boat on that budget is totally doable and I say this from experience. I've done it twice. My first boat was an S2 9.2 and cost me roughly ~$14k including repairs and refitting a lot of the boat. My second was an Ericson 29 at about the same cost. Keep in mind that I did ALL of the work myself. It was hard but rewarding.
Find a good boat with a solid reputation and foundation. Do the research and only consider boats that have been well cared for. You will pay for other peoples mistakes. And lastly, look at a lot of boats! This will give you an idea of what you want or don' want in your boat.
Good luck in your search and if nothing else, you will learn a lot.