Since it's not your daily you can go as crazy as you want with mods but whether you should depends on your mindset. With myself I never plan to get rid of my car, it'll likely be taken off the road completely one day, I don't care about being the fastest or best car out there, and money isn't a concern so I'm just going crazy with it. With the right mods these cars are a ton of fun but at the end of the day it's an inherently flawed platform and there are cars out there that are far quicker bone stock or with one or two mods. In autocross I have a friend with an NB Miata that cost him $3000 to buy, fix, and get tires for. It's bone stock except the tires and he's faster than me. On the track I'm in the advanced group with the kind of cars you mentioned in your first post. The quickest car is a BRZ with Enkei RPF1's, some kind of sticky tire, and AP Racing brakes. With all I've done E46 M3's and STi's still put distance on me through the corners and the BRZ laps half the group. I can close the gap but these cars are just built to do this kind of thing so they'll always have the advantage.
Based on what you've done so far don't do anything else to the engine. You need tires, brakes, and suspension. Michelin PSS are good tires, I went from Continental all seasons to PSS and it was mind blowing how good they were, so don't feel like you wasted your money. Next time you go to the track or autocross take chalk with you and mark lines on the sidewall. When the tire rolls over the chalk gets worn off and it shows you how much it rolls so you can add pressure. There's a groove maybe a quarter of an inch or less from the tread that you don't want to roll past, if you do you need more pressure. Use the PSS until they're worn out and then try the Hankook Ventus R-S3. Running 35 psi they don't roll onto the sidewall at all and the difference you felt when you went to the PSS will be the difference to the R-S3's. The problem the PSS has is they made the sidewall soft to be comfortable and quiet on the road since so many cars have them from the factory. With a car that has 50/50 weight distribution that's fine but with so much weight up front it really limits your ability to turn in.
For brakes I'd recommend stainless lines, DOT5 race fluid, and upgraded pads. And for suspension a Koni/spring combo and sway bars. To give you an idea of the difference it makes when I first had my coilovers put in they were set soft, by doing nothing but changing the damping to the factory preset I gained 10km/h on every straight. Now imagine if you were able to brake later into a corner, had tires that could turn in harder, and suspension and tires that could hold higher lateral load. You'd also be able to get on the power sooner coming out of the corner. It won't make you instantly faster because you'll need to learn the new limits and work up to them but once you do it'll change everything about how you drive. You'll also notice that even though you don't have more power it feels like you do because you weren't able to use it effectively on stock suspension. I wouldn't do more than that to your car until you've decided how committed you are to it. It'll be a huge improvement but a Miata/BRZ/S2000/M3 will do it right out of the box or with less investment in parts. Keep the stock parts, drive your car for a few years, and if you decide to get a better track car put the stock parts back on and sell everything.
As for holding people up, if a car is behind you it's because they're quicker so if you see someone in your mirrors just signal and let them by. You don't need to be on a constant lookout because a slower car will never be in that position. Check your rear view mirror as you enter the braking zone and as you start accelerating onto the straight. While you're on the straight you should be on one side of the track so just check the opposite exterior mirror every now and then but mostly listen for other cars, you'll hear the engine of any car coming up on you. Until you get into the advanced group you're only allowed to pass on designated straights so if someone's behind you anywhere else just focus on driving clean and making it to that straight safely.
How do you prepare your car before a track day? Do you check anything yourself or take it to a mechanic?
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