"What to look for in a new boat?"
Well, I would suggest bouncing on the deck to see if that is shot / squishy.
Check the hull for damage.
Check the interior for signs of deck leaks.
Check the standing and running rigging
; and winches
for grinding (unmaintained sounds).
Run the edge of a quarter across the threads of the sails. If they break easily, they're shot.
Spin the propeller
shaft to see how true it is, and wiggle it to check the bearing(s).
Look straight up the mast to see if that is straight.
Check the wiring, where it is hidden away, to get a "feel" for how corroded it is throughout the boat.
Look at the backs of lockers / cupboards etc., to see a lot about the overall condition.
LOOK AT THE BILGE!
Check the engine, run it from cold, and see what color any smoke is.
TEST / TRY every single device and equipment... to use in your negotiations... do the toilets work, sinks drain, windlass
work, A/C work, refrigerator & freezer working? REally?
Check the bilge and water supply pumps
The navigation lights
Any hydraulics, (steering?), the rudder (which will be wet), and did I mention check for a squishy deck... ? :-)