You would need to do at the very minium:
1) New front lower control arms
2) New Rear Upper/lower control arms
3) Subframe connectors (if you don't have any)
4) Lower profile sidewall tires (you can choose the size of the rim depending on your braking capabilites)
5) New shocks /struts
Now for the extras:
1) New tubular front K-member
2) strut tower brace if your car is convertible
3) remove as much weight from the car without turning it into a racecar that you drive on the street
4) a nice set of gears
5) new seats with lateral support to hold you in the corners
I prefer a manual tranny for carving corners to get just the right RPM at entry / exit of the turn
That should get you started and really lighten the wallet
I just bought a set of GMS upper and lower control arm, Ford motorsport lowereing springs, and KYB shocks for my 86 GT. That really woke it up. I was extremely impressed with the difference the rear control arms made. The rear is super stiff now. I need a strut tower brace to even things out now.
The Mustang's biggest problem with the suspension is the rear 4-link. Great for drag racing, sort of, but not good for handling. If you really wanna handle the curves, I would look up Maximum Motorsports or Steeda, perferably MM and see what packages they have.
Just a UCA/LCA package would make a world of difference. It really changes the difference in the stability of the suspension.
I just finished installing the Bullitt Suspension on my 92 GT and some new FMS Lower A Arms and a set of SFCs and the difference is amazing. The 5 Lug conversion helped too with the slightly wider track!