I'd check the sails carefully for any boat your are considering. New cruising sails for a 36' boat (main & genoa) would set you back about $5K, if you are going with a name brand. I'd have a sailmaker inspect the sails that come with whatever boat you are considering. If you stay below 30' the cost could be less than $4k for the pair.
It's not just the sails that wear out, but all of the other stuff that makes a boat work. You may want to consider allotting 10% of your budget for repairs/replacements. Even if you capture a well-found boat, stuff happens. If the boat has had structural repairs, I'd run--not walk--given your budget.
Another thing: asking isn't always getting when it comes to price. You might check the boat Blue Book values for any boat you are considering. At least you'll get an objective opinion on worth.