Decks decks decks. Check the decks for signs of wetness and rot. That's the most likely major problem although there are plenty of others. I agree with your engine reasoning.
As for the survey it would be more for piece of mind than financial reasons. Picture yourself sailing with your family and friends 2 months from now when the weather turns bad. You'll feel better at that moment if you had the boat and rig
surveyed. That's the biggest reason in my mind for a boat at this price point.