Start with better brakes and suspension. Even better, just buy a car with a bigger, faster engine that already has the brakes and suspension to suit the power. I know that goes against all the dreams of turning a little car into a quick little car but it's cheaper in the long run, unless you are an engineer and an engine tuner and have access to your own workshop and rolling road.
I'm not being negative, just honest.
The most important factor in any power performance upgrading is the ability to STOP, next is the ability to be able to take bends. Prior to all that is the ability of the driver to control the car itself.
Do I still sound negative ?
I'm not, I'm still being honest. I've seen far too many people put far too much power into cars without ever thinking of stopping the damn thing or how it will react on that wet bend with worn suspension and semi bald tyres and lack of ability to drive the car on a dry road, let alone a wet slippery one.
I would hate to deter people from doing things with their motors because, after all, that's why most of us are on forums like this. I just want some people to be realistic, step back and think about all the aspects involved instead of jumping in blind and wanting everything to go faster.
Don't forget that a car that handles better and stops better, is also a quicker car, unless you're driving on completely straight roads.
Good luck with whichever path you choose but please, consider all the aspects.