At your high end of $15K, I'd probably consider a survey. At your low end, probably not, if I did a fairly decent inspection and checked for delamination (soft and "mushy" spots on the deck, coachroof, cockpit, etc.), obvious evidence of leaks, large cracks, holes, etc., and checked the running and standing rigging for wear and anything looser than it should be. If you have a friend who is knowledgeable, bring him or her along during your inspection. Ask the owner if he or she would agree to a sea trial to check the engine and how the boat sails and handles.
At the high end, you don't want to spend half-again as much (or more) as you paid for the boat in repairs to get it seaworthy. The money you spend for a survey would be worth it. You may want to resell the boat some day for something newer and/or bigger and you need to satisfy yourself that you're get your money's worth.