Do some good searching through this forum. Naturally, this question has been asked several times just really depends on what direction you want to take the car first. Personally, I think suspension is really rewarding, which is what I'm doing first. You can do power mods inside that budget and make some decent gains. Without going F/I you won't make big power of course and thats a bit above what you are looking to spend.
take a look through this thread
What did you do to your BRZ Today? and get some ideas of what people have done.
If going suspension route I'd recommend (like he said above) some better pads at least. I bought rotors/pads/lines/fluid because after 1 track day it was clear the car needed better stopping power. Also there are a lot of spring sets out there that are real solid and very affordable. Wheels/tires are also popular because the stock tires are really not very great in the grip department ha
For power, I'm not as knowledgeable but the little reading that I've done looks like doing full exhaust, filter, e85 and tune can easily get around that 200whp mark which is fun in this car. I did a catback only at this time because the car is too quiet for me lol
