YES... a tuned WRX can easily leave a standard STI in the dust -- all about how much is spent tuning the WRX
On Classics the engine is pretty much the same engine and minor mods and a remap will see similar or better power on a WRX over an STI with comparable reliability. Of course other things like suspension and brakes will need some attention.
On Newage cars it is less straight forward as the WRX and STI engines are quite different. Some minor mods and remap would definitely see similar or slights better power figures than a stock STI; though if going for big(ger) power the STI engine will go further without spending big money to ensure reliability. Things like gearbox, brakes and suspension again may need attention - though keep in mind parts are easy enough got to do a rolling upgrade as you find bits.
Lads are right that probably the best value right now money vs performance and at your buget, is in the Bug STI. Deffo, don't look for the cheapest you can get -- it is worth spending 1000-2000 more upfront to get a really clean car in great nick compared to a really cheap one that will break your heart, and cost 3000-5000 over time to put right. There isn't a great market out there for these cars, so you can afford to be picky and leave the "dogs" to get a clean one!
"Red Top" doesn't mean a whole lot.
BTW... It actually is the intake manifold that is painted red.
There are quite a number of power outputs for engines with red manifolds from the factory... and at this stage many stock WRX engines have been painted to appear to be something different from what they are.
What will give you a better indication is looking at the engine type number and looking it up online to see what power it came with. Similarly the chassis number can give you a better indication (if you verify that the engine number on the VIN plate matches the engine that's fitted). Obviously many engines have been upgraded and mapped and in that case you want to see a graph that lists the VIN/Reg and also lists if it represents numbers on RON95, RON98, or booster etc (don't just take graphs as gospel and ask the right questions to verify numbers).
Good luck with the hunt for the right car!