With your budget and requirements, put cruising catamarans on the list of boats to examine. Here's a link to affordable boats.
Catamarans for sale by owner
Remember because catamarans are wide boats, they equate to a monohull approximately 50% larger. So, for instance a 38 foot cruising catamaran would have equivalent living space and stowage as a 57' monohull. Yet be easier to handle and more live aboard friendly. A 40 ft catamaran would have 3-4 cabins, 2 bathrooms, be bright and airy and they don't heel while sailing.
worth a look...