On a budget, my thoughts.....
Decent struts, KYB GR-2/excel are a little better than stock, and reasonably priced. Get an alignment after install.
Decent tires, type depends on where you live.
Tire pressures, cheapest handling mod out there. My starting point (assuming decent tires) is 80% of max inflation as molded on the tire sidewall. Then, vary the front/rear split.
I can deal with "TTO" (trailing throttle oversteer), so I run most daily drivers with about 6psi more in the front than rear.
Auto cross on tight courses, I run 8-12psi more in front. More open courses, I run a bit more than daily.
Track days are different, laps generate MUCH more heat in the tires. Spirited street and auto cross generate less tire heat.
Pressures come up about 1psi/*F.
Front drive and most AWD cars are set up to understeer, I hate that but it's safer for most drivers.