Does your car have a properly installed, unbroken, front sway bar? A missing or broken sway bar or link will lift an inside rear tire all day long while the outside front corner mashes hard into the ground....

Really need a $$$ budget to make any feeble attempt to answer your opening question. Are you looking to drop $500 into this project, or $10,000+? Or somewhere in-between? And we'd very much need detailed info on what your current setup is, and the present condition/age of ALL your suspension and chassis parts...particularly bushings.

I frankly found a drastic improvement...surprisingly flat cornerning...after simply replacing all my bushings with polyurethanes, upgrading to a heavy duty aftermarket front swaybar and links, and replacing all my tie rods, ball joints, and steering/pitman arms with factory-style MOOG stuff from local auto parts store. I then went for a test-drive and it was absolutely night and day comparing before/after the rebuild.

That made everything tight and new, with some additional improvement over stock provided with the fat swaybar and poly bushings.

The other big wild card is the condition/age of your subframe/body bushings. If original, they desperately need replacement and they have a HUGE impact on handling. This is often cheap and reasonably easy to do, depending on your rust situation. If rust-enlarged holes are found in the process or your cage nuts spin and the bolts don't come out (both very common), this is going to be the true root of your problem, and no amount of aftermarket bolt-ons will stop your entire chassis from flexing and destroying your handling...in which case you need to prepare yourself for the beginning of a subframe-off resto to fix it properly. After confirming the holes are properly sized, your options for these subframe bushings are factory rubber, poly, and solid. And subframe connectors will offer yet another drastic improvement to these cars, costing anywhere between a reasonable $150-ish for bolt-ons and full blown multi-thousand-dollar (due to labor intensive if you don't fab and weld yourself) floor-integrated weld-ins.

After doing my above-mentioned mild front end upgrade and repair, it later led me to a full restoration, and I now have solid body bushings, floor-integrated weld-in connectors, poly everything-else, etc. Car is a rock...I couldn't get it to lean into a turn even if I wanted to anymore. And it also dialed a great deal of the comfort out of my ride. So beware of trade-offs. I intend to do some occasional rally road-course racing and such, but haven't yet. Comfort/smooth ride is not really a major concern for me. Might be for you. Makes a huge difference in what you might decide to do. As one very mild example, many have installed poly bushings only to find they hate them...others swear there is nothing better.

But for all we know, you might simply have a wear and tear problem, or an improper alignment, and simply fixing these issues might satisfy you quite swimmingly, depending on your perspective, desires, and how badly your car handles right now.

As stated earlier, this is an extremely difficult question to answer, because "improve the handling" is an infinitely subjective phrase that means incredibly different things to different people, there are still an infinite # of answers to the question regardless of how you interpret that phrase...