Howdy!
I have a '16 GT convertible, Perf Package (the tire above is going on that car), slowly getting less stock, so I can definitely answer your questions about tuning (this also being my Nth something performance car as well)
I'm assuming you're on some Mustang specific forums, if not, sign up,
www.mustang6g.com is fantastic, great technical resource, mostly friendly and helpful people - lots of events, sources for used and new parts, etc.
Like most modern engines, the current 5.0 is undertuned, under-exhausted, etc., to account for emissions (especially during startup), warranty, noise levels. Very light bolt-ons like an air intake (whether a full CAI type, or an aftermarket tube+filter) and an exhaust will gain only gain a touch of power. Where the 5.0 makes huge gains - relative to the effort/price - is in a tune. Most cars with an intake/exhaust/tune, are picking up a solid 40-50HP (they seem to average ~410 to the rear). Add long tube headers to that, and you're over 500HP (430+ RWHP), plus nice additional TQ, especially across the midrange. There are some "quiet" exhaust options, you'll just need to research some of the "touring" models, that tend to be near OEM quiet and can be managed via the throttle.
If you're squeamish about warranty concerns that might be introduced with an aftermarket tune, Ford offers warrantied performance packages:
https://performanceparts.ford.com/performance-packs/#m2016
Not as aggressive as aftermarket tuning, but kind of "no worry"
Otherwise, there's a HUGE option for tuning from Lund, Steeda, LMR, Livernois, and dozens of outstanding smaller shops you'll have to research in your area (I use one of the best in southeast, who happens to have a shop 5 miles away).
From there you can get as radical as your wallet will support: GT350 / Boss intake manifolds / TBs, for a full tilt NA build, or what the 5.0 really loves: forced induction
A buddy of mine just turned his own wrenches on a supercharger install, a SL2200 Paxton kit, did it over the weekend, running 130+ MPH in the 1/4!
With a base GT, I'd also look into some suspension, again Steeda can help, along with companies like BMR. Aftermarket springs (for both handling improvements AND aesthetics, stock cars look like trucks ...), swaybars, endlinks, cradle kits, bushings, etc., lots of things that make a big visual difference like aftermarket wheels, but also affect performance.
Anyway, congrats, have fun!
