How much would it cost me to build a fast car?

I had a question… My mom has this really old 1995 Ford Taurus she's thinking about selling it this car is really beat up from the inside no dents from the outside though the engine is pretty bad but it still runs its been her daily driver for about 5-6years she wants to sell for 300$ but I wouldn't want her to let it go for that much and I was wondering how much it would cost me to basically make this a fast little son ***** pull the back seats out and everything
I wanted some recommendations on what engines and transmissions were good to fit this car v8 preferably with a budget of around 3-5k

What do you define as "fast" first of all.

Secondly, the Taurus could be a decent performer if equipped with the SHO engine and the 5-speed manual. But the regular V6 models were not designed primarily for performance. A V8 swap is physically possible but you would still be dealing with a FWD platform and you would need to significantly strengthen the rest of the powertrain to handle the extra power. In the end, it would still be a nose-heavy FWD platform and that hurts handling.

Remove everything under hood that says ford(engine and transmission) replace it with a gm 350 engine and transmission

The only V-8 engine that would fit a Taurus is the Yamaha engine that came in the Taurus SHO, and THAT is becoming a rare commodity. If your Mommy only wants $300 for her POS automobile, then that's about what it's worth. Don't waste your money.