if you can stuff a 15x9 under your arch with some pulling with a 245/40/15 r comp that would be my choice
i will be running a 15x8 +32 with 10-15 mm spacers next with 225/45/15 hankook rs3 v2 next
i run 15" wheels with 11" discs all around on 15x7's and a fairly expensive suspension setup, worth about 3grand usd
poor handling is generally down to poor damping, lack of travel (the car barely has 3 inches stock, bc racing and shitty coilovers have like 1inch of bump travel), and tire choice
the less unsprung weight you have the better, if you need the large brake kit then of course 16/17's
but i like the low weight, inexpensive tires and rims in the 15" size. they give you low rotating mass, less unsprung weight which helps handling, braking, acceleration.
in north america the list of tire of choice for performance use not including track r compounds is in the 15" rim size are 195/50, 205/50, 225/45
bridgestone re11a (soon to be replaced with the re71r) (had the older re11 Not re11a, good steering feel, good in wet, not great cold and not great hot)
bfg r1 rival ( soon to be replaced with a new compound) (not my favorite in the old spec, lacks outright grip and not great from cold)
hankook rs3 v2 (my favorite tire on heavier vehicles in hot temperatures, not great steering feel a bit mushy but best out right hot temp dry grip)
toyo R1R (soon to be replaced with a new compound) (driven several hundred laps on these on various cars, my fave tire awesome cold and in wet, but get greasy if over heated, which it does quite easily in autox competition, lacks a bit of steering feel with a soft sidewall but u can run a shit ton of slip angle)
dunlop z2 starspec (ok in wet in the older z2 (non ss compound), but doesnt like cold and wet, good steering feel)
falken rt615k (driven on these not my favorite tire, pretty terrible in wet)
advan neova ad08r - never driven