when you say track worthy, do you plan on taking it to the track for fun, or do you wnat to compete in a specific class. the answer to that will drastically change my answer on where to start.
personally, i'd say oiling upgrads are the FIRST thing you should do. and not just changing to a better oil. the brz likes to oil starve in higher g corners. so swapping for a killer b or iag oil pan/pickup is going to be a key thing here. i'll admit i'm not super familiar with all the oiling issues they have, so i'd look into if the pan/pickup/baffling is enough or if you need more.
from there, upgrade the brakes, a decent street but track capable pad is going to be key, something like stoptech sports. and upgrading to a higher temp brake fluid, such as a motul rbf660.
after that, i'd focus on tires and suspension, a decent set of aftermarket wheels with a 200tw tire will improve lap times quite a bit, more so than doing a full exhaust by a long shot. though it is nice to hear the car under the helmet on track, for that, just a catback is needed.
suspension, start with a quality set of coils, plenty of options for these, but expect to spend 1500+ usd. cygnus, fortune auto, ohlins all make quality parts. i'm sure there's plenty more for an entry level set, but these are the most popular brands, at least in the USA.
after you have that dialed in, THEN i would start worrying about power. from there you may find things like seats/harnesses and such may be more beneficial than adding power. or aero and weight reduction if you go that route.
also, early on, even if all else is stock, i would get the car tuned just so it's going to be super safe on track.
if you wnat to compete in a specific racing class, i'd be looking at class rules before any modifications. as some of what i listed above can put you into different classes, at least in the USA.
