Tire compound vs width

I have a 04 ep3 with factory 16x6.5 rims I'm looking for some tires that I can use on the street and occasionally on a track for road corse. This is not a dd but something to have fun in on and off the track. I live in nc so snow is not really a problem and dropping below 30° is not a big deal.
what I am trying to decide is if I should move up to 17s in the long run but for now the question is which tire I should go with on the stock rims.

I'm looking at*
Kumho ecsta pa51 at 225/50r16
Federal 595 RS-R 205/45R16
Toyo*PROXES R1R 225/45ZR16
Falken Azenis RT615K+ 225/50r16
I'm trying to keep things on a budget I have had the handbook v2 on the car before and in hard coners at speed they would brake loose a bit so it seamed compound or with were defiantly needed as the were 205 55 16