Sadly it has only 215 HPs, I said sadly because at 1999 Ford upgraded to 260 HPs.
"Much" faster without great budget is not possible, its not a fast car to start, but, you can change your final drive ratio, thats relative cheap and give you much more acceleration, but will reduce your top speed.
You can try other mods using a car performance simulator there you virtually tune you car and see how it improves after mods, try at http://www.nxgtrsim.com
Was something like 215, if I remember right. The weakest link in your two valve is the head air flow, so that will show the most improvement. There are two ways to go - Get the '99 & later PI factory heads & port them, or step-up to the Trick Flow aluminum aftermarket heads. Guessing porting the PI heads & adding some decent cams will get you up to almost 300 horses. If you go with the Trick Flows & cams, maybe towards 340 hp. The Trick Flow heads are like a grand, & cams are like $ 700 for the pair. I've seen PI heads for sale on e-bay. If you go too big on the cams, then you'll need some stronger valve springs, too. Those are like $ 150 for the set. There was just an article in the Mustang mag I get about working on the two valve engines.
225 HP. The 1998 model has a slightly better flowing exhaust, and a slightly more aggressive ECU tune than the 215 HP 96 and 97 models. As far as mods go, A P.I. head/intake manifold swap will be the best bang for the buck, it's an easy way to gain about 40 HP, if you go that route you can also add some hotter cams while you're at it, you can save on labor if you do both as the same time.