I bought a poor condition AW11 as a project car. No regrets so far, but it's taking plenty of time and a realistic budget to make it good.
An enthusiast owned car with new suspension, engine swap, 15" alloys, performance tyres, nice paint (etc) selling for 5.5-6.5 K$ is selling at the upgrades cost. A scruffy at 1000$ leaves a budget to work with to fix whats wrong or improve (my situation) but is never going to stay "cheap". Avoid a 2.5-4.5 K$ car which looks ok at purchase but then needs a similar fix-it budget to the scruffy.
The Denso EFI is early generation (like a Bosch L) with basic morse code error reporting, not OBD2. So troubleshooting is with a multimeter not a laptop. It took me around 2 hours to pin out and confirm everything was in limit.
There's lots of support on the internet with the factory manuals, part number books, purchase guides and specific "how to's". The supply of mechanical parts is still excellent. Ebay, SCA & Bursons all support it as you are in the Corolla parts bin. Amayama Jap direct imports will cover you for almost everything else at excellent prices provided it fits in a small package and you can wait 2 weeks. The plastics everywhere, especially those exposed to sun, engine heat or snap fit are getting brittle. So go slow and careful. Anything on the front 1/3rd of the car can be scarce and is more expensive to source compared to a MX5. Missing pin striping on my bumpers was a tell tale of accident damage fixed on the cheap.
The "mid engined" aspect needs special consideration. Bad alignment or worn suspension are not items you will want to ignore as there is a possibility of unsafe handling, not just poor handling. Fuel pump failure is common and complicated by the mid engine location. Mine took 2 days and required pump/screen/filter/filler hose and an injector clean. The AW11 EFI plastics/rubber is incompatible with E10 fuel.
Japanese body steel seems to be of excellent quality. Keep an eye out for superficial rust, serious rust seems to require salted roads.
SteveB