Pre-buy after Annual

Newcomer to group and ownership here. Hope this isn't an FAQ, but Googling
the keywords brings up too many hits that don't address my question.

I'm looking at a fairly typical first plane to buy ... 1960s Cherokee ...
that appears to be just right. It has reasonable airframe time and low
engine time. It was annualled two months ago.

My specific question is ... Since the plane was just annualled, what should
I look for in my (free, amatuer) pre-buy and ask the mechanic too look for
in the professional inspection, that would indicate a "don't buy" decision,
even if the annual is fresh.

I'm thinking about things like interior wing corrosion that are airworthy
this year and probably next, but would make the plane a poor long-term
investment.

Is this the right question to ask? Experienced, non-monetarily motivated
answers appreciated.