Welcome aboard. Spend some time before the actual survey and poke your nose into every compartment and see what it looks like. Make notes and ask the surveyor to look at the things that look odd to you. Ask questions of the surveyor, this is a good time to learn about the boat. Good luck!
Attached is a checklist that might help you organize your thoughts.
I like the Hershine 37 - almost bought one about 30-years ago. 20-years ago, I met a couple in Baja who were headed to the Caribbean in one. Nice liveaboard for a couple.
I assume you are in the purchase process - if you have not done a sea trial yet, make sure the engine is run-up to wide-open-throttle (WOT) for at least 5-mins. The owner should provide the captain to run the boat (often the broker). Fuel tanks are always a possible issue on an older boat, especially one with teak decks They can be difficult (impossible?) to inspect, but ask your surveyor to make extra efforts. Thinking about it, a boroscope (remote camera) might be able to be wedged over the engine room insulation to view top of tanks.