1983 gtsi 12k

Where are you? Some places require all original smog equipment and check for it, others check tailpipe emissions only, others have no checks. The missing equipment could be expensive to replace if needed in your area.

Check service records. Check to see when the timing belts and tensioners were replaced, whether the water pump was rebuilt, what other work has been done. An 83 GTSi may be a quattrovalve car, verify precisely what you're looking at because there's a price differential between the 80-82 GTSi and the 83-85 GTS QV. The 83 has some unique parts, there's a recent thread in this section about that.

Check the condition of the seat bolsters and the pedals. The odometer is easy to disconnect on the car, so make sure the condition matches the mileage.

If there's a local Fcar mechanic, have the car inspected

 

like Tillman said, it all depends on where you live or are going to live and whether or not they have emissions testing.