[strat61caster]

Top choice: Miata

Heard a story a few weeks back about a guy competing in some amateur series, he always did ok, middle of the pack fighting to break into the top, he took a year off, bought an NA Miata and got as much seat time as he could, came back and was a force to be reckoned with. The Miata teaches you like some Yoda Initial D shit, your mistakes are obvious, the car can take the punishment, there will always be an answer to your problem/question because the community is so long standing, and it can blow the doors off a bad driver in any car if you're on your shit. Spec Miata record at Laguna Seca is 1:45 (cheating notwithstanding), that's a ~$10k build with nearly stock power levels (130hp or less) if you're smart, toss some power into the equation and go check the Motor Trend Drivers Car of the Year lap times.

Edit: I now dream of the double wishbone fully adjustable off the showroom floor suspension in a Miata after spending a thousand bucks and counting on my 86's alignment.

Here's a couple options I would personally do in no particular order, be forewarned, all of these would be project cars, they'll have bugs to work out, they are old and parts are hard to find, they would never be perfect but should be fun to toss around for not a lot of money. The miata is objectively better but these have a bit more character and charm imo. I also would budget no less than $5k to hit the track and plan on spending up to $10k to get everything dialed in, safe, reliable, and tuned to my liking.

E30 (just to pile on, E30 M3's are $30k+ for non rust buckets), ideally get a 325i and beat on it, 160hp and ~2,400 lbs isn't too shabby and swapping into an E36 M3 motor has been done a thousand times if you want to dump money into it, good for ~240 horses there's a pretty serious one locally that's badass.
Edit: E36 M3 could also contend, also maybe a Z3 Coupe? The M Coupe is up around S2k and used 86 pricing so that's a no go but that's also on my shortlist.

MR2, mid-engined goodness, Toyota reliability if you're smart, personal preference is AW11 (MK1) but the MK3 is probably the best for most purposes, and lots of people love the SW20 (MK2), I don't think you can go wrong with any of them.

RX-7, FC/FB, not a lot of power but Mazda sold a fuckton of them because they were great sport coupes for the time, a naturally aspirated 12A/13B is proven to be stout and durable and respond well to bolt ons, what other engines need an expensive camshaft to accomplish a rotary can gain with a dremel tool. I've heard the FC has great suspension that stacks up well to this day, the FB however has an archaic live axle, it can definitely be effective but lacking compared to a true independent setup.

Porsche 944 (924 maybe), probably the most expensive to get to the track but also the most rewarding, a big boy Miata if you get a non-base engine, and even with a base engine should be more than capable. If you can find a late 944 S2 it's basically an 86 with an I4, hatch, Porsche parts prices, and more displacement, ~2,800 lbs and 200hp NA.

Mk2 or Mk3 Supra might also be a contender but never really looked at them in depth.

FWD often gets overlooked but can be a blast on a budget: Integra, Civic, CRX, RSX, Prelude, maybe even Del Sol for Honda, Celica for Toyota, always GTI, and recently new Mini's have caught my eye, R53's have a cult following now and the R56 is just dipping into 'cheap' territory.

And if it wasn't painfully obvious yet, I love momentum cars, no ungainly V8's for me, give me agility any day of the week, I'd rather loose 4 car lengths on the straight and gain 4.1 in the corners any day of the week, hell even less and wait to capitalize on a mistake.

/armchair quarterbacking

Edit: S2k is expensive imo, wouldn't budget any less than $15k based on what I've seen locally, and ideally I'd budget up to $20k. Can buy an 86 at that point which only needs brakes and alignment to hit the track (vs. the unknowns of a 5-15 year old sports car sold at a low price for a reason), ideally some camber and eventually tires for the 86, which in OEM size aren't bad at ~$600 a set.