First thing is to get the car checked over properly.
No point in going if you have 1500 miles left on your pads as you will put a 1000 miles on them there and back, plus say 8 laps will kill them quickly. Also have any oil leaks, split CV boots or anything else you find fixed - there will be a very big bill if you break down on the ring.
So first thing is to make sure brakes have plenty of meat, and tyres have plenty of tread.
On that note, make sure you ahve good rubber - not mismatched makes or super cheap tyres - they are the only thing that physically holds you to the road, so make sure they are good.
Next step a service - nothing huge but fresh oil (and a decent make oil - the crap you buy from halfords will not be protecting the engine as well as better oils - its the same as buying a cheap loaf of bread - its the same thing as Hovis but the taste is much different - same with oil, just because it says 5w 40 on the bottle does not make it as good as an Ether based 5w 40 like Fushs titan pro S - whcih is what id recommend and what I use)
So now we have fresh oil, decent tyres - next brakes.
If you wish to upgrade then pads are most important - if your discs are worn/lipped then look at replacing them too. the ring doesnt tend to be too bad on brakes, but saying that iv killed a set of standard Clio pads there so upgrade if you can - not to improve your braking time, more to keep you safer and less prone to fading.
Dont forget brake fluid - old fluid will boil very quickly so get it changed.
Dont worry about rear brakes, they do very little so as long as they are in good condition then leave them be.
So we have fresh oil to help protect the engine, decent tyres, and decent brakes.
This will make a big difference on a 10 year old car, and to be honest id be very happy with a Clio in that state of tune.
You can upgrade more , but a 1*2 in a good state (ie with the above done) will be great fun.