As mentioned above in message #7 tires are critical when it comes to handling. That would be the first place I would look when trying to improve handling. Sadly, there isn't much of a selection of good handling tires available in the stock rim sizes. I wound up having to switch to 18" rims to allow me to get the tires I wanted. Some people don't like the look of the larger rims, but I am pretty happy with it and it allowed me to get the Michelin Pilot Sport 4s tires I wanted in the widths I wanted.
My above statement assumes that your stock suspension is in good shape, bushings not worn, ball joints and tie rod ends not worn, steering box not sloppy, etc. From there, I would look at adding anti roll bars (also called sway bars) and better dampers (shock absorbers). I went with Firm Feel for the anti roll bars and Bilstein for dampers on my 1969 Coronet. Since my original steering box had poor feel and quite a bit of slop (and leaked like a sieve), I replaced it using a Borgeson box purchased through Bergman Auto Craft along with their steering coupler. This box provides a very nice steering feel and almost no play (at least I can't feel any) in the steering. I also increased the size of my torsion bars (Firm Feel) to 1.00" which I feel is plenty for a street car. If you have anti roll bars, the torsion bars don't need to be that large, as the anti roll bars will deal with body roll and the torsion bars just need to be stiff enough to keep your suspension from bottoming out when you are driving. Hope this helps you in your planning, Cheers!