Understeer is going to steal loads of laptime, as will brakes that don't inspire confidence.
For handling, try the following (in this order):
Front camber - 1.2-1.5 degrees for fast road and heading towards 2 degrees for track
Uprated rear anti roll bar, but be careful - go too far it it can get quite over-steery (although this can then be managed with the throttle) 23mm or 24mm max
Coilovers and cornerweighting - the Coupe (especially the 20VT) is quite uneven left to right and responds well to being properly set up.
Quaife differential - it will transform the car - as soon as you feel a bit of understeer, assuming you 've got the space, just plant the throttle and some wizardry will pull the car round. It's spooky and often makes passengers go pale / quiet...
Brakes
The standard calipers are capable of stopping the car perfectly well - don't bother spending a fortune on uprated calipers. Its all about heat management (and the 20VT is poor for this). Get some Fiat 500 695 Brembo floating discs and thank me later - they are epic. You'll also need some pads capable of handling north of 750 degrees. I swore blind by Pagid Yellow (RS-29, I think). You'll then need something good on the back, otherwise the rear will try to overtake the front unless you're braking in a perfect straight line (Coupes don't like trail braking very much...) If you can find a way to do it, rig up a cold air feed to the centre of the inside face of the front discs. It'll probably work on a track car, but I could never work out how to do it on a road car.
I spent several years and more money that I care to remember making a 20VT handle - it can be done, but it ain't cheap. The Coupe is a Fiat Tipo in a posh frock and it was never designed to perform well on track.
I documented a lot of it (albeit road biased) in this thread:
https://www.fiatcoupeclub.org/forum/ubbthreads.php/topics/1601490/coupe-handling#Post1601490