What fluid are you using? Nothing could be worse than doing 3 laps and have the pedal go to the floor because you boiled the brakes. Even new fluid will boil after a few laps so make sure to use a race fluid like those suggested (Motul RBF 600, Castrol SRF) and try to use the same pads all around putting a race pad in the front and a street in the rears will make the fronts do even more of the work and can cause them to overheat early.
Of course your tires were awesome at the track, it was your first day. Now that you have a benchmark, a set of cheap used semi slicks will really blow your mind. The limiting factor in breaking is usually the tires. Put the best and biggest brakes on a car with shit tires and it wont stop. Remmeber your contact patch between your car and the road is only a few square centimeters so the better grip on that patch, the more stopping power your brakes will have.
The best way to go faster is driver training. Spend a few laps following the experienced drivers, try to get in for a passenger lap and do a training day. You would be amazed how much faster you will go wen you learn to keep the car settled and balanced.
In my time attack Evo 7RS we focused on getting the brakes as efficent as possible while retaining the stock brembos. We reduced as much weight from the car as possible, less mass to stop. Reduced rotational mass (lighter wheels, 2 piece rotors, allow wheel nuts) to put less rotational strain on the brakes. cooling ducts to the front bar to help drop the temps as fast as possible. To top it off I used Michelin slicks for absolute grip (and lighter than road tires).
Now that the swaybars are done you will start to consume some parts and I would look at mods over time in this order:
1. inspection and bushings, replace any worn or broken bushings get under it and look for wear. check brake lines ect. You don't want a sloppy car at 200km/h
2. RBF 600 fluid (costs less than Castrol SRF)
3.track tires and wheels (so you dont tear up your road tires)
4.alignment (get the most out of your contact patch)
5.better brake pads all around (Im a fan of Ferodo DS2500s for a street/track car, 3000s for track only)
6.new rotors, the track pads and temps will eat or crack the stock rotors after a few days
7. Coilovers (Racing Logic, Tein, Ohlin or others with a motorsport background)
8. chassis bracing (keeps it aligned under cornering load)
Good to see some new guys getting out to the track and using their cars for what the designers intended.