Hi and welcome.
I would assume any mods will be declared to your insurance (otherwise you'll be driving illegally and if the worst comes to worst you will be prosecuted) meaning that anything you do declare will no doubt sky rocket your insurance premium. So my first piece of advice is not to bother until you're older and have a couple years NCB.
But, if you really have to.
The 1.3 itself isn't really worth modding. You'd have to put in a bigger engine. However, a cat-back exhaust system and a panel filter (don't bother with an induction kit) will give you a better throttle response.
Don't be cheap when it comes to tyres as well. Budget means just that. Get the good stuff you'll be rewarded. Better rubber means better grip, better handling, better braking etc.
I would also upgrade the suspension. A 1.3 Fiesta will never be 'fast', but it can be fun. The right suspension set up will allow you to enjoy the car better. I would get some coilovers (at least height adjustable) to get the lower and handling better. A front strut brace is also something low cost and easy to install, that will tighten up the front end, again improving handling.