Sold my '13 FR-S recently (owned it for over 8 years) and it was one of the best cars I've ever had... still don't like boxer engines and won't ever get another one (I've said this twice before...) Put about 63k miles on it and never changed suspension from stock, it was getting about time to refresh it though.
From '15 onwards they changed the suspension/neutered it's playfulness to make it more neutral/less tail happy, aftermarket mostly seems that way as well though there are a few options that more or less keep the original F/R spring rate ratios of the FR-S (the BRZ was always less tail happy, from 2015 onwards the FR-S & 86 handling approached that of the BRZ tune.) I would have only gone with a setup that kept near stock spring rate ratios of the FR-Ss first two year as I loved how it feels and was not chasing time. There are plenty of options though for those chasing down time wanting something more neutral, Racecomp Engineering springs would have been the route I would have gone if wanted to make it more neutral, quicker on track. Dampers no matter what would have either been the Bilstein B6s or Koni Sports as I don't want adjustable coilovers.
Also, stiffer engine/transmission mounts will make the ride quality much better at speed... the Perrin motor and transmission mounts I switched to noticeably improved chassis over bumps/ surface impacts - stock mounts really let that wide boxer motor flop around and you can feel it. Going to stiffer mounting is like switching from a bit worn out shock to a new one, much better control of the rebound after the initial impact coming through the tires, no secondary oscillations in the chassis, just a single solid impulse.
I will say this, going from stock wheel & tires to lighter 17x7.5 on smaller 205/45-17 Firestone Firehawk Indy 500 was one of the best changes I liked for daily driving. Instant lower CG and 4+ lbm reduction at each corner (stock 17×7 wheels are near 21lb boat anchors), with shorter tire diameter which gives a more responsive feel to right foot input (both accel/deccel). For track I still wouldn't go beyond stock tire size in a sticky compound - a good lightweight 17x8 wheel with nice stock sized DOT-R tire (Nitto NT01 would be my preference).
The best change for seating position was the 949 Racing 50mm factory steering wheel extender... no more compromise in seating position between whether the hand or foot gets short end of the ergonomic stick, can get both right where they need to be. Gets even better with a seat that works unlike the factory seat (not a fan of the factory seats, very uncomfortable for me for anything over 20-30 minutes). 949 Racing 50mm extension made the factory seat more bearable (when sold the FR-S the buyer wanted the stock driver's seat, so it went back in after many years of a nice Recaro Sportster CS that fits me WAY better along with tying you directly into the chassis.)
Cooling is the main thing you have to worry about... engine bay retains heat like an oven, anything you can do to remove heat will be appreciated by the coil packs and oil... consider coil packs a wear item like tires if you track it. Adding oil cooler and baffling the oil pan a very good idea for a track focused one. Also recommend venting the hood towards the front and venting the side fender garnishes. And if running a front license plate absolutely remove it on track. Brakes could also use cooling... there are duct kits (Verus Engineering in particular) or the more expensive brake kit options. Always wanted the Essex Racing Sprint front brake kit - nothing like really improving your brake systems thermal capacity while dropping 10lbm of unsprung weight at EACH front wheel... $$$$ though.
Also, if not on stock exhaust, an aftermarket exhaust will actually present an issue with less rear stability than stock at high speeds due to how the large factory muffler is used to direct airflow out the back. Two ways around this... cut off the fake diffusor section that is catching the air and unsettling the rear or get/make a diffusor that works with the stock fake diffusor bumper section to control the air better. I cut the fake diffusor section off on mine because my exhaust burnt a hole in it (from a cracked tip seam)... less weight, makes the rear look slimmer, and free.
Oh, always do the pedal dance or get something like the Trac Box.... traction control is annoying on this car (at least it is on the 2013 I had.) Also not sure if it still applies to newer ones but the rev limiter was really bad on my 2013... like at all costs (if not in pedal dance mode) you don't want to hit the rev limiter... very hard cut in power that absolutely sucks on track. I just set the rev light and alarm to 7krpm and shifted there just to be sure to not hit the limiter whenever I forgot to do pedal dance. The pedal dance / Trac Box is absolutely what you want to use for track work.
