These are good choices of iconic 90's japanese sports cars but why automatic?
Automatics back then were crappy and couldn't handle the power thus if any models had automatics there were crippled "shampoo cars" in today's language it would be "poser cars". I'd suggest you go for newer models with DSG if you want performance cars with automatics.

2004 Nissan Silvia - this one comes under budget however it is a 2004 car, getting a loan might be tricky. It looks like a private seller so you've gotta do all the leg work of getting documents from him and submission to banks, jpj, etc to get your car. Usually, for me I'd rather do it myself when dealing with private sellers to avoid issues/conjobs. If you've got friends working as car salesman you can get him to help you out, if you're lucky you can get a normal loan 10% deposit 90% loan.....worst case scenario is cash deal.....but usually if it is just pass the 10 years old mark you can still get loan but maybe not 90% maybe 80/70%. Anyway, if you like it quickly track down the seller as automatic S15's don't come around very often in the market as most people love this car for its looks, power and drift capability.....so it is 99% of the time a manual.

1997 Toyota Supra - Supra is going to be quite old and expensive (3000cc engine - imagine the roadtax!) to maintain, not going to be easy to find and buy as it is always going to be a cash deal because of it's age. If I am not mistaken the automatic will always come without a turbo. IMHO it is going to be too much to be worth it unless you're going to keep it as a 3rd car for collection sake, maintenance would be high for a daily runner, this is better to be skipped.

I don't see any s2000 under budget and their mostly manuals anyway.

I suggest the models below....

2007 Smart Roadster - new enough to have updated safety standards and technology but old enough to be affordable. This is a chic roadster, it doesn't come with a big engine only a 700cc lump to power the whole car, which doesn't sound alot but this car has been built like a Lotus which means the concept of lightweight chassis and good handling. If you want a coupe with sporty looks that can overtake other cars at highway speeds or traffic light drag race this isn't the car, however if you enjoy Sunday drives up and down winding roads like Genting Sempah, Genting or old trunk roads this is a blast. A similar car but cheaper would be the 2006 Mg TF

2013 Honda CRZ - would be similar to the car above, it isn't all about power. However, the big differentiation between this Honda and the two above is maintenance. While the two above would be affordable or expensive depending on the workshop and items that need to be repaired, Honda's as we all know are more on the affordable side with a 1500cc engine similar to the one found in the Honda City it is not going to be a maintenance nightmare unless the Hybrid system breaks down, the newer models such as CRZ have a long warranty period for the Hybrid IMA system and have more affordable pricing for replacement parts.

The 3 models above are compromises yet don't give much performance for the money spent, if performance is what you want see below....

2012 VW Polo GTI - it is a 2-door coupe as you wanted, turbo as you wanted, DSG with paddle shifting automatic gearbox......the only blackspot is that this is 1400cc + 7AT DSG which is notorious for breaking down. I suggest going 1up to 2008 VW Golf GTI which I think is the car that has it all except for being 2-door for you. GTI's with their 2000cc turbo and 6AT DSG's aren't known for breaking down. However, if you insist on performance+2door+auto then my last offer to you is 2005 Mini JCW and for your budget there are alot of models and ages to choose from which can get confusing anyway to make it easier the turbo ones will always have an air scoop with the S logo.....the best of them are JCW variants.

Maybe you could narrow your search and we can chat more about it?

They're good cars if you only consider the performance side of things but when you consider age, loan capability, spare parts and maintenance cost you then have a more rounded idea of how much budget you really need to own one. I mean if RM88k can buy a sports car without drawbacks everyone will be driving around in one and not a boring box like a Vios. 

The few I chosen for you are newer, more fuel economical for their power output and easier time getting them serviced (higher reliability).

If you don't mind 4 doors the Altezza is a great car with alot of potential, get the one with the BEAMS engine.