Stock calipers only work if you drive it slow. Plan on a BBK up front at least. Not sure if used C6Z brakes are a better deal, fit or worthwhile compared to aftermarket BBK's.
I have a C6Z which suffers many of the same weaknesses as the C5Z. I love the OEM brakes though. Good feel and pad wear, no fading on 100tw tires. On the rare occasions I take it to the track, I drive it pretty quickly.
-Big brakes can restrict wheel choice which affects tire choice so plan ahead before pulling the trigger on brakes.
-Coolant runs hot so plan on a better radiator.
-Oil temps run hot so plan on slightly heavier wt oil and at least a small oil cooler. I run Amsoil 10w40 street oil with a slightly larger reservoir which keeps temps/pressures happy for 3-4 laps in the hottest weather.
I'd need a proper aftermarket cooler with -12 lines to last a full 25 minutes in hot weather.
-Trans runs hot. If you are still learning and not going to run full 20 minute sessions at maximum pace, you might get by OK w/o a trans cooler. OTOH, if you plan to run bigger R comps and are a fast consistent driver, plan on a trans cooler.
-The LS6 is a pretty bombproof engine provided it has a good oil supply. It will oil starve in long turns but isn't as sensitive as the LS7 in the C6Z. Accusump is the easy fix.
Full race setup involves an aftermarket dry sump or extensively baffled/gated wet sump with external pump.
The level of prep for HPDE in any production car is a mix of the platforms inherent weaknesses and driver ability. A newb driver in a Miata in cool weather needs a roll bar and helmet. An advanced driver in a C5Z in hot weather is going to drop $12k before it's really bombproof.
While that may seem like a lot, keep in mind it'll still be a sub $35k build that will smoke a lot of high dollar equipment with the right driver. If you have the budget, over prep it. If you are on a tighter budget and know you won't drive it to its limit, you can economize here and there.