Fredo, you don't say whether or not you have any previous sailing
experience. You can certainly learn the necessary skills on a boat in
that size range but if you don't have any previous experience sailing,
then you are not in the best position to evaluate the decision of sail
vs power. The vast majority of people living aboard and cruising in
sailboats spend very little time actually sailing. It's a fact. A
small trawler in the mid 30 ft range will have vastly more liveaboard
space than a sailboat, and be a great deal more comfortable. You will
also end up with better fuel and water tank capacity and room for a
decent generator, all of which are generally lacking on sailboats of
that size.

That said, there are plenty of people living and cruising on mid 30s
sailboats. One of the better ones for that purpose in my opinion is
the Pearson 365 but there are others as well. Look for a heavy
displacement boat with good tankage, a solid diesel engine, and
generous accomodations/storage space. Shallow draft (less than 5 feet)
is a plus also. Plan on spending at least 20 to 40% beyond the
purchase price for equipment upgrades. Typical improvements would be
such things as a high capacity alternator, spray dodger and full
bimini, solar panels, wind generator, high capacity battery bank,
upgraded refrigeration, inverter/charger, RADAR/Chart Plotter, auto
pilot, sails, etc.