Turbo vs Nitrous vs Supercharger

No way your going to get a working s/c for 300.. try more like 2000-3000

That filter kit thing is the worst way to spray IMO.

get an NX wet kit at shop.hyundaiperformance.com :

A high-quality turbo alone would cost more than a grand; and you've still got the wastegate[if it isn't internally gated to begin with], manifold, dump pipe, cooler pipes, boost controller, and vac lines to factor in. Unless you're going full-on DIY and second-hand, third-rate parts from a wreck pulling it off is going to be very, very difficult.

I'd go with the Nitrous kit for that budget.

So should I get the one sugested above or one from ZEX? Also, is a Transmission oil cooler a good idea for $100 shipped?

yes and yes. Ive never heard of reliablity issues with NX but ive heard many problems with ZEX.