All of the above. These things are not specific to the J, or to aircraft in general. Mooney tanks are wet wing. There is no bladder from the manufacturer. The sealant has a life span. It breaks down with aromatics in fuel. Mooney tanks WILL seep over time. Seeps can be more of a cosmetic nuisance than a safety of flight issue. There are dedicated tank repair vendors that will get them better than new for $5AMU's per wing. Budget for this. Bladders (weight penalty, but likely won't ever leak again) are a second "option".
Fire wall Forward: Engines get hot. Cylinders and accessories (Oil Coolers, Magnetos, Plug Harnesses, Oil Lines, Alternators, Mufflers etc.) ALL have a service life. If the engine has more than 1,000 hours or ten years plan on some of this stuff needing replacement/repair. If the engine was overhauled did it get new/overhauled accessories? What was not done? New cylinders?
Landing gear biscuits wear out. This is NOT a big deal if your tanks are already seeping and they aren't falling out of the gear (loose) J's although medium body don't have the weight of later long-body Mooney's. This is a detail vs. a deal-breaker on your J Model.
Avionics: Latest and greatest is...Great. Let someone else put in the Garmin center stack and wizz bang engine monitor with fuel flow. You can get these (Installation is expensive) for .50 cents on the dollar installed. ADSB is coming....A few thousand to get compliant.
J specific wants: -Later planes had enclosed wing tips, speed brakes, removable rear seats vs. a bench. Can take one or both seats out or fold them down. THIS IS AN AWESOME FEATURE THAT I WISH I HAD...Plus the cabin extension that the F also has.
If your J has lived in Florida (and many have) an extensive inspection of the airframe for corrosion is a MUST DO. THIS is the kiler of Mooney's...Benign neglect.
Later J's have a much improved overhead ram air supply for passengers/crew.
Buy a well maintained mid-80's to newer J after having it inspected and choosing the corrosion free Garmin Wass'up equipped airframe with the paint that says "you" on it and watch the ground go by at 150+ knots on 10GPH....
Enjoy the hunt!