So, with a really old car, I start from the general proposition that I need to identify the critical stuff in the car, and then either know when the critical stuff has been replaced or I plan to replace it.
With a car like this one that is really good cosmetically, it is highly likely that the mechanical aspects of the vehicle were attended to; review the records to determine when critical items were last addressed.
I use Rob Siegel's Hack Mechanic book to help me identify the critical stuff. The two major take-aways I can recall from Rob's book were: (1) check the components of the vehicle electrical system (including the ignition system) and (2) review the cooling system. If critical items within these systems (like the battery) have not recently been replaced, replace them or, if you are like me, have a plan to deal with them.
With a car that looks this good, you are going to have some judgment calls to make. For example, if this car has its original alternator and it has been tested and is still working well, you have a tough call to make. The car should warn you if it begins to fail, and most such failures occur gradually. So, you could leave well enough alone. Or you could consider picking up a working backup, refurbish it over time, and then swap it in before the one in the car fails. This is what I did.
After these two big areas are addressed, move on to other items that could leave you stranded. Rob mentions fuel delivery as a possible "leave you stranded" item. Go over fuel hoses and lines and filters and fuel pumps. And don't forget the gas tank.
Suspension ball joints and tie rod ends also come to mind as leave you stranded items, although these usually give you warning if you pay attention to the signs. Here again, with a car like this you might leave well enough alone.
And, while brakes rarely leave you stranded, I always evaluate the braking system any time I buy a used car. (Actually, assuming I was able to drive the car home, this is the first thing I do. I have a thing about brakes).
One final overlay on top of this. While the car may look great, consider the useful life of the materials that originally went into the car. For example, my car came with the original seat belts, but the useful life of the webbing used to make them was 25 years. Counting on them 45 plus years later would not be wise.