One of the first things to update is the tires. For handling, it's all about how well the tires stick to the pavement and the tire selected makes a huge difference. Unfortunately, it seems like the best handling tires also tend to require larger diameter wheels (many people don't like the larger wheels on the classic cars, but I am getting to be OK with it up to a point). I am in the process up putting new wheels and tires on my 69 Coronet, and I wound up having to go to 18" wheels to get the tires I wanted (Michelin Pilot Sport 4S) in the sizes I wanted. Regardless of the other upgrades, a car won't handle well with poor tires. Tire Rack has some good info on tire selection. I haven't received my new tires yet, but I have the same tire on my 2008 Saturn Sky, and have been very happy how sticky they are.
That said, there are a number of suspension upgrades that are typically recommended. I would prefer to stick with torsion bars rather than a coil over setup due to the lower weight distribution (lower centre of gravity, less roll in corners) and the fact that they are all sprung weight and that the factory suspension was engineered to be rugged and long lasting. Typically, a spring wheel rate of about 10% of the front end weight of the car is considered a good starting point for handling. You don't want to go any stiffer than what is necessary to prevent the suspension from bottoming when hitting a bump in a corner. If the spring rate is too high, you tend to lose traction on bumps because the car has started to move upwards and the weight comes off the tire as the car comes down the back side of the bump. I went with 1.00" bars from Firm Feel, which have a wheel rate of 175 lb/inch and have been happy with the ride quality.
Replace the dampers (shock absorbers) with some good quality ones. I went with the Bilsteins from Firm Feel. They are tuned to work with classic cars. You can get adjustable dampers, but adjusting them for best handling is best done during repeated timed runs on a racetrack. It is very difficult to set up the correct adjustments otherwise.
Front and rear anti-roll bars (also called sway bars) are an important upgrade. This is the correct way to control body roll, not by using stiffer springs. You will want to but the front and rear bars from the same supplier as they will be matched to work together on your car. Sometimes you can get and adjustable rear bar so that you can fine tune the handling to your liking, but that will require some careful testing and adjustment, preferably on a racetrack. I went with the Firm Feel solid bars. I chose Firm Feel partially because their rear bar is frame mounted, which slightly reduces the unsprung weight at the rear. This is probably unnoticeable, as the weight of the bar is a tiny fraction of the weight of the rear end assembly. I also had to reroute my fuel line around the mounting plate.
Replacing the upper control arms can be a good idea as the stock one were designed for old bias ply tires and it is not usually possible to get enough negative camber and positive caster with them. I went with the Firm Feel ones because they use the factory style bushings. I am not a fan of using Heim joints in the suspension because of concerns about them picking up dirt in the joint and wearing.
Replace all of the front suspension bushings. Original style rubber work well but are not as stiff as polyurethane. Polyurethane requires greasing, however (they tend to squeak when they get dry). They are also a wearing part as there is sliding contact on them. Most people seem to like the polyurethane.
It is probably a good idea to get the lower control arms reinforced. This is recommended if you go with large anti roll bars, as the front bar cause a twisting force on the lower control arm which the reinforcement helps to resist. I haven't got mine done yet, but plan to get it done this winter.
I went with the Borgeson steering box, which has a faster steering ratio (14:1 vs 16:1) than stock. It also is nice and tight, as it is brand new manufacture. I got the kit from Bergman Auto Craft since he includes an adaptor that allows the Borgeson box to be installed without modifying the steering column. The steering in my car feels much tighter with the new steering box. Lots of people have said good things about the Firm Feel rebuilds as well.
I also replaced all of my ball joints and tie rods and ends.
I have also heard a number of people recommend sub frame connectors, but I haven't installed them (yet) so I can't give an opinion on them.
Overall, I have been very happy with the mods to my car, but I won't be able to form a real opinion until my new wheels and tires are installed. Looking forward to that a lot. I would be delighted if it would eventually handle as well as my Sky, but I doubt that is in the cards. It's fun to try, though. Cheers!