Okay, lots of shit advice in here so I'm going to add to that with my 2c.
If you have a 20k budget, I'd be in a S2k in a flash. 2L NA manual vert that does 270kmh stock is pretty bloody impressive. (Not that you should test that out..)
As for the more realistic cars, NA skylines are boring as batshit, not to mention slowww!
Autech S15 DE = Waste of money like skyline NAs imo. (So expensive too)
I'm a fan of 300ZXs but I know most here aren't... Still going to leave this here: Clicky Me 170rwhp stock is a pretty decent effort... Plus targa = girls
Supras. I do like them and the manual NAs go hard for what they are. You could get an aero top auto, then convert it to manual, especially with the budget you've got, maybe twin turbo swap down the track after Ps.
E36 BMWs are nice, just got to get one thats been looked after. I had no troubles with my old E36 M3. Off the shelf TT & SC kits are available...
If you have some old school taste, you could go for something like this: Click link
Or cause your budget is so big, you could get one of these: Click linky
Those are all the good RWD suggestions really...