The TR-7 was constructed as a simpler car than the previous TR's; not simple in terms of primitive, but simple in terms of technical complexity. Being British, Triumph substituted less reliable electrics for reliable suspension and engine components.
The '77 model shared a lot of components with the Spitfire 1500 and the Austin Marina. The problem was that it was a heavier, more powerful car than the Spitfire, so some components faced heavier use [and thus less life] on the 7 than on the Spit. The second problem was that some of the shared components from the Austin Marina were based on low cost, not sports car racing potential.
The nice thing is that you have the Rover 5-speed, a strong transmission that uses a stronger, Salisbury rear end. These options eliminate two problems common to early TR-7's. When the engine is cold, the transmission gear oil that usually comes with the car gets very thick and beats up the synchros. Rover and Land Rover specialists that share the same transmission recommend substituting ATF for 80-90W gear oil. You might have a slight graunch from 2-3rd, but that would be it once the car warms up. ATF lubricates well and runs thinner.
The 2.0 liter engine runs very well and for a long time. However, early ones tended to overheat when the cooling system was not cared for. Flush it often and be generous with quality anti-freeze. When they overheated, they blew the head gaskets. Since the engine block and head are different metals, they proved hard to separate to replace the gaskets.
Change the oil and filter often [3,000 miles]. Check the front wheel bearings [they're small for the weight of the car and easy to replace].
Structurally, it's a monocoque body structure so the 3-part sills, front and rear bulkheads, and shock towers must be sound to be safe. Some body parts are still available. Regular maintenance items - filters, brake pads, brake cylinders, shocks, bearings, alternators, starters, are easily available from a variety of speciality [Wedge Shop, WedgeParts, Moss, Victoria British, Roadster Factory] and generic suppliers [NAPA, Autozone].
Since 1989, I've owned and used for daily driving a '78 Spitfire and my current '80 TR-7. On both cars, I put about 75,000 miles each. They've had their share of maintenance repairs and have left me stranded for short times. The TR-7 is vastly superior in ride, handling, speed, control, speed, trunk space [the Spitfire needed a luggage rack, it's superflous on the 7]. I've loved my two Spitfires but it's a budget car compared to the TR-7.
Buy the car. It sounds like a great buy, even at the asking price. I'm looking at a '77 also and I wish it were that inexpensive!
Jeff