Which car have you purchased and why? If you were to do it over again, what would you do differently?
I've owned nine Supras total. Kept the very first one I bought and then started diversifying the collection to include Mustangs and Corvettes and Jaguars. Supra was my high-school dream car but I couldn't afford one then. When they came out in 82, I'd ride my bicycle to the Toyota dealer and drool over them till the salesmen ran me off. Had to wait till after college and bought a used 85 soon as I'd saved up enough money. I didn't know then that Supras would become an obsession. We call it MSS (Multiple Supra Syndrome). If I had it to do over again, I'd have instead of buying more Supras, I'd have bought some of my other 80s high-school dream cars while they were still affordable in excellent condition, like the Starion ESI-R, the Nissan 200SX turbo, Isuzu Impulse RS turbo, ASC McLaren Capri, Merkur XR4Ti, etc., etc. Now I can't even find them in fair condition.
What should I be on the lookout for (good and bad) on these cars? What parts are made of unobtainium?
To the extent that these cars share parts (engine/transmission) with other more common Toyotas, its not too terribly hard to keep them going and stopping. But we are starting to see some issues with Supra specific parts like in the rear hubs and differential. The unobtainium stuff is anything made out of plastic, rubber or vinyl on the body or in the interior. Do NOT buy one thinking you are going to restore it. Pay more up front and get one that you'd be happy to take to a show or whatever you plan to do with it as-is. You can do minor rust repair, paint and leather upholstery (tho its more expensive than the car is worth), but you can't buy replacement trim or weatherstrip or anything like that.
am curious why some cars seem to do better than others with potential buyers.
There is a HUGE price variation from MINT being now near $30,000 all the way down through PARTS CAR at a few hundred dollars. Reason being is you can't restore one. If you want MINT for a museum piece, you gotta find one and buy it that way. You want EXCELLENT for show purposes, you've got to find one and buy it that way and they pretty much go for half of MINT. You want GOOD which is about the lower limit of what you'd ever take to show off at a local cruise night, you've got to find one and buy it that way and again they go for about half of EXCELLENT. Now you might be able to take a GOOD example and repaint/reupholster and get it up to EXCELLENT, but it would cost more than its worth. There's really not even a lot in FAIR condition at half again, but by that level, they are so bad your only option is to go full pro-touring where you're building a whole new totally modern car on an old shell. Thus people won't pay much for FAIR or worse.
Is the P-Type more desirable than the L-Type,
In the U.S. the P-type is more valuable as it was specifically developed for the U.S market. The rest of the world got the L-type body and in some foreign markets, our P-types are considered a little too "boy-racer" for local tastes.
is the 5 speed more desirable than the auto,
Yes. Generation X was really the last generation that learned to drive stick (due to learning to drive used muscle cars) and the Supra was the new car Gen X cut out of the magazines and taped to their lockers. So of course that stick shift is part of the nostalgic driving experience. A little of it too is that automatic transmissions weren't all that great yet in the 1980s either.
is original better than restored,
I'm a bit biased as a card-carrying member of the NCRS and MCA. I love an original car. But there so far doesn't seem to be the same level of interest in absolute originality with Japanese cars as there is with muscle cars and earlier coach-built cars. I think a lot of it has to do with the era they were built. The US government in the 1970s had imposed emissions and safety restrictions that far exceeded the available technology of the time. Since unlike the 60s muscle cars, you couldn't buy a factory "big block" Supra or any other Japanese sports car, and because horsepower was roughly half of the used muscle cars Gen X was already driving, it was a little more acceptable to make modifications. By the late 90s, the technology was finally catching up with the regulations so now you can buy a Hellcat that passes emissions, but that's what we were faced with in the 80s. So in short, I think our collectors are at least right now, mostly OK with performance modifications as long as they are well done and documented.
I don't know what the future holds tho, so if you do plan on performance modifications, just don't throw any stock parts away, don't cut, drill, weld, glue or paint anything such that it can't be undone. As long as the car could be returned to stock with a couple of three-day weekends worth of work, then you preserve that possibility for later in case that's the way values swing.
Now there have been lots of discussions on this forum in the past about various body and interior modifications and I think its pretty safe to say that with the singular exception of aftermarket wheels (more on that in a bit), there is a general consensus that a stock appearance is more valuable. There were some aftermarket body kits but P-type was already leaning toward "boy racer" and those kits were even more extravagant. Its a niche taste, and it doesn't really seem to command a premium. Again, value is about nostalgia and collectors will want a Supra that looks exactly like the picture they cut out of Motor Trend and taped to their locker back in the day.
Wheels tho are a bit of a practical matter. There's really only one tire in the stock P-type size and back to the "more power" we also needed more "more grip" and more "stop" to go with it. So its a perfectly acceptable modification to install 17" wheels to fit a larger brake rotor and/or just to get a decent selection of tires. But remember, value is mostly about nostalgia so modern wheels that don't look right could be a deduction in value. Best to go with period-correct looking wheels. Again, keep the stock wheels in storage just in case.
are the 1984-85 cars more desirable that the 82-83 cars...
85-86 was the ultimate evolution of the mk2 with the most features, alarm system, auto headlights off, little light around the keyhole and probably a few other things I'm forgetting. 86 changed the stereo and added the 3rd brake light, but I think that brake light looks tacked on like an afterthought so to me, the 86 is just slightly less desirable because of that. Other people could care less about all the nifty features because they don't like the spoiler that was added in 1985. But in general, the last year of any car model is usually the most valuable because by then they'd worked out all the bugs and added all the features that they were ever going to add.