To increase the performance the first thing to do is to make it go around corners more quickly. This means better brake pads, better damping and accurate suspension settings.
Then the overall weight should be reduced if possible.
After that consider improving the engine specification to increase the torque.
A better cylinder head is the key to improved performance. When I first got it my 1990 Cooper had 33.5 mm inlet valves. I just fitted a slightly gas-flowed MG Metro head and put the CR up to 10.2:1. The flywheel was lightened and it now has a pre-Verto unit. The HIF44 carb was improved and a twin-box RC 40 exhaust system was fitted. I put in a 266 cam (well, MG Metro one, but they are irtually identical). The distributor I changed for an Aldon Yellow.
Once set up on the rollers it gave peak power of 84 bhp at 5700 rpm and peak torque at around 4300 rpm.
I also fitted a 3.44:1 FDR to improve acceleration.
For the road that is quite enough and anything further will reduce the driveability of the car and tend to make it 'fussy'.