Adam you do speak a lot of sense! If I wanted to go faster in real terms on the cheap, I'd get some springs to stiffen it up, and strip it out! will help with the braking, acceleration, hell even MPG
As Des said, people often just stick on bigger brakes without renewing the tired braking system in the first place - the only thing I would warrant an upgrade with these would be brake pads!.
Once all that's done, get is setup correctly, there's loads of places that sort out the alignment and setup of your car with lasers and shizzle (or the old fashioned way which is apparently better) these days - makes a world of difference if done right!