Nothing wrong with the Base GT if you're willing to do a little work, namely the Performance Pack's brakes. The factory cooling on the PP is nice and cool, but most people who get serious end up upgrading, and if you're coming from a Base GT, you can either pick up their factory stuff on the cheap, or just do what they're doing just the same. Base GT factory suspension sucks, but you can get a FRPP Track Pack to hang with the HPDE crowds, or a set of motorsport coilovers to compete. Since you're towing, with a little patience, happen to know your way around salvages, and have some friends, you can have a full car for under $20k. Since it was until just recently the current platform, just about all of the factory parts are still well available, so most boo-boos can be fixed without a long downtime. With all that speed and weight, you'll chew through expensive tires... but that's pretty much the same for all in the bigger bore classes when compared to a Miata, 944, e30, etc.
For me Base GT preferably on the cheap could be the best option since you want to ditch a lot of the things that make a PP1 package (Just not enough of that is worth it for a serious track car). If you are trailing the car you can up your brakes game a lot and get rid of the PoS "Brembo" and buy real racing brakes, good coilovers, since you are doing your cooling anyway you can ditch the PP1 radiator and get better radiator from the get go. Regarding suspension skip all the strut and springs combos and move straight the MCS 2 way ot Cortex JRi. Overall here is how my dream build should look like if it's strictly a track car:
1. Brakes:
ESSEX/APRacing:
13.01.10119 - $5700 - Fronts
13.01.10120 - $4599 - Rears
This are what is fit on an FP350s so they should be good for track
Braided Brake Lines and Clutch Line - $400
Some form of front brakes cooling - $500
2. Suspension:
Front:
Either MCS TT2 or Cortex JRi both are around $4300
Steeda Front Swaybar + Steeda Competition Swaybar - $700
Whiteline / Steeda Endlinks - $400
Steeda Front Control Arms + Tension Links with Bearings - $700
Steeda Bumpsteer kit - $240
Camber Plates Vorshlag - $525
Rear:
Steeda IRS Base Kit: $209
Steeda RLCA Bearings: $240
Steeda Toe-Links with Knuckle to Toe Link Bearings: $375
3. Engine Cooling
LCR-50-96 0-4063 FP350S Oil Cooler: $600
M-6675-M52RR 12 qts Oil Pan: $1503
M-6675-M52RR Oil Pick-up Tube: $195
M-8501-M52A Wather Pump: $229
Mishimoto MMRAD-MUS8-15 Radiator: $647
Mishimoto MMTS-MUS8-11 Thermostat 160: $60
Some form of Radiator Ducting
RaceLoover Hood Vents: $600
4. Wheels + Tires:
Apex EC-7 19x11: $2000
Goodyear SC3R 305/30/19 - don't know the price in states
APR Studs Front: $120
OPMustang Spacers: $50
OPMustang racing lug nuts: $50
Other than that you can round up this build as you like with engine mods (not very familiar there as I'm running stock motor for reliability / ease of fixing) and Exhaust / Intake. Same goes for safety items like cage, seats etc.
Overall from what I'm seeing on my daily/track car the biggest issues for a MT82 car is brakes cooling and CHT temps of the engine some of the mods in the cooling are overkill but I'm a huge fen of the pay ones cry ones methodology.
Hope this helps.