Studying 1st Stage and 2nd Stage, and being a mechanic, I've got the formula. Well, most of it. You'll need to fine tune it, but here's your recipe!

Main Ingredients
One Hachi-Roku (AE86. Try 1984-1988 Toyota Corolla.)
-Make sure it's a 1.6 TwinCam (4AG) and manual. Try for a GT-S.
A really deep pocketbook - for a poor guy, Bunta is spending a LOT on parts.
An account at Toysport.
A good buddy at the Toyota dealer.
Someone who can make you a 'Fujiwara Tofu Shop (Private Vehicle)' sticker - optional.

1st Stage - Some Like It Mild
Take Hachi-Roku.
Add these parts available from Toysport or Toyota:
Toyota Japan 48511-AE881 - Four Way Adjustable Front Shock (pair)
Toyota Japan 48531-AE881 - Eight Way Adjustable Rear Shock (pair)
TRD Japan Front Springs 2.8kgf/mm
TRD Japan Rear Springs 2.7kgf/mm
TRD Front Sway Bar
TRD Rear SR5 Sway Bar
Cusco Front OS Strut Bar
Cusco Rear OS Strut Bar
TRD Bushing Kit
TRD Short-Shift Kit
Clutchmaster 16-029-HDTZ Stage 3 Clutch Kit (includes all parts)
TRD Limited Slip Differential, Rear, 1.5 Way or 2 Way (to preference)
Toysport Fender Flares (shouldn't need them with the GT-S)
}Toysport Trueno (Kouki) Front Bumper Assembly (check if you have fog lights first.)
}Toysport Trueno (Kouki) Rear Bumper Assembly
Order as a package, includes Trueno emblems! (WOO!)
TRD Red Spark Plug Wires (optional)
TRD Exhaust Header (black TRD is accurate, but you can get ceramic.)
JIC Bullet 505Type1 Exhaust System (50.8mm tip, but 90mm pipes - the BIGGEST.) - Cat-back package!
Toyota Japan Oil Cap - Totally optional, but it's cool.
TRD Engine Mounts - ABSOLUTELY NECESSARY
Good pads and rotors - may I recommend Raybestos? (It's cheaper than TRD.)
... by now you notice we haven't done too much to the engine. What makes the Hachi-Roku so fast? It ain't Takumi alone. It is tuned - from the factory. Japan gets 102 octane fuel (I am NOT joking) while we're stuck with 93. Toyota reduced the compression on the 4AG for the US market, which reduced power drastically. Nobody seems to make a conversion kit. So you'll need to either play around with camshafts (TRD, TODA, Toysport) which can get expensive, or you can call Toysport and get a 4AG JDM, or you can go with what you have.
What's this get you? About 100% improvement in handling. But you're still missing something. The wheels.
Here's where it gets tricky. I can't tell you for sure if those are Panasport FS Formula 1's painted in black, or Watanabe Type F8's, or Watanabe RS8's, or Watanabe RSes. So I studied stills for a while. They're not Watanabe RS8's - no polished lip. They're all black. So, where does that leave you?
I'd recommend Panasport FS Formula 1's in black or Watanabe F8's. The Watanabe F8's are probably more accurate, but are 15x8". The Panasports are 15x7". Either will fit the 86, both look right, both are upgrades. Go with what you like.

Mmmmmm.. tasty! Best served on twisting mountain roads in rural areas near you.

Or buy a Scirocco and or Corrado and whoops some ass. Cuz if you know what your doing, a nice VW can own almost anything on the road. (Im personally in the midst of rebuilding my 84 Scirocco. )

don't count on it. the corrado g60 is heavier than it looks. the scirocco can't run as long as we do, or as hard. neither can keep pace. none of the folks i run with, run 86's. we do have two ae92's, 4agze powered, and modified by experienced toyota guys. a lightened ae86 with a 4age formula atlantic (this is what bunta installed in the 86 in 2nd stage) could keep pace, but only barely.
it really comes down to how much you want to spend. a 4age formula atlantic is about $10,000 alone. a 4age formula atlantic in an ae82 would have no problem beating the pants off a g60. but that's why the ae92's went 4agze.

That parts list reminds me of when someone converted their Eagle Talon (Basically a Mitsu. Eclipse) to be a drug smuggling car... Except they got Carbon Fiber for the WHOLE thing... But Man, that thing woulld GO!

hahahahah that's sick. sad thing is, that really is a very very mild car. it'll handle like a totally new beast, but still very streetable. trd has some really insane suspension parts available, that i'm sure were used for the 2nd stage car. (post ep11.) 8.4kgf/mm springs, 18 way adjustable shocks, anti-roll and anti-sway bars as big as the rear axle! cool stuff.

g60 Coroddos are nothing compared the the VR6 Raddo, As for sciroccos, they can keep up with anything if you maintain them well and know what your doing. They are light, agile, and depending on mods, VERY fast. Someone pulled 350hp out of a stock 1.8l Scirocco. And Corrodos, not sure how much people pull out of those, but depending on options, Corrodos are not that heavy.

it's my understanding that the corrado also comes in a vr6 flavor. but let's put this into some real perspective, before it gets out of control. (or we have a civic owner come in here claiming he beats corvettes.)
one, it comes down to driver more than car when it's short.
two, it comes down to car as much as driver when it's long.
three, the guy with the most money and most knowledge wins. always.
now, remember how i said bunta must be rich? let's do some math, shall we? first off, the stock 4ag has probably been warmed over. cams and valves. that's easily $2,000. the springs probably $500ish. anti-roll bars, $300ish. shocks were probably close to $1,000. bushing kit is easily $100. short shift is something like $300 if it's close to the ae92's. the list goes on and on.
long story short, on paper, the 1st stage hachi-roku has at least $4,000usd in modifications, minimum. it's likely to be much higher. it's also clear that save takahashi ryouske, the drivers are not all that skilled. 2nd stage, better drivers, and pretty much a whole new hachi-roku. 4age formula atlantic, that's $10,000. then the computer, another $1,000. new transmission, $2,500. easily well past $15,000.
and someone comes along with a $90,000 viper, and blows his doors off.
'show me the money.' that's what wins the races.

Yes but, building up your own car, and racing within the same class have all there own benefits. You know your car better then the guy that just got the Viper. A good cam, and tuned head would run me around $200, Exhaust, $300. New engine for a little extra power, $250, Spring all around, what was it.... $150 or $200. Don't remember, been looking into it lately. Stress bars (Lower/upper) around.. $200ish, Roll cage? Still debating on that. but I could get one made for around $200 if I wanted one. Mostly, prices depend on the car. Some people charge a lot more for mods for newer cars, and older cars, they don't. Even tho you could pull the same results from that. I could go Turbo, or get Supercharger, or even NOS, But personally, I want to keep it natural. Anyway, you don't race cars that arn't in the same class, unless you KNOW you can win.