I used to work at a boat marina for three years. I could help a little.
Have you owned or been around boats before? If not be prepared learn learn alot even if you how to work on cars.
Things to look for: Is it a jet drive or a I/O?
Check for the bellows(rubber boot) if they have dry rot or even holes. Turn the drive fully to the left and the right.This will expose any holes(I found this out the hard way.) Ask the owner for the last time they were even changed. He should say once every year or two years at the least. If not CHANGE them. You should not get cheap here. It's about $80 for parts verses a sunken boat recovery charge.
Also ask if when last time was the water pump replaced.
Was the engine ever over heated? If yes, DO NOT even think about it just go.
You're doing good checking compression. Check for all the other things like old, glittery, milky motor oil. The same goes for the outdrive oil if it has one. Most boats do not have a radiator so nothing to check there.
Take it on the water for a test spin. NEVER ever ever turn on the boat without water unless you want to replace your water pump. Listen for all the obvious things first. Then when you take off listen for a noise like a skate board wheel on concrete. This could be your gimble bearing going bad if it is an I/O.
When things are okay take for a full throttle test run. Listen to the engine for hesitation or stumbling while going fast. This is how the mechanics test them anyway so why shouldn't you?
That's just a few of the less obvious things to look for and L'm sure I left some out but that should get you started.
