There are several things that you want to look into. There are a lot of safety areas that you don't want to skim on. Road racing gets expensive quickly.
-Most importantly is that you upgrade your brakes and brake fluid which I don't see you mentioning. Can you race with stock brakes? probably yes, but if you are going to be driving at 100mph+ in a race course and braking hard at the corners I suggest you go with the biggest brakes you can afford. I don't know if you still have rear drums but I suggest you upgrade them. Once you upgrade the brakes or even if you don't, make sure all the brake lines are in good condition. However, since they rot from the inside out it is very difficult to know their condition. I wouldn't race on of these cars without first replacing all the brake lines. The last item on the brake system list, but probably the most critical is to completely flush, and I mean completely, the old brake fluid and replace with a high performance DOT4 fluid like Motul 600.
-For suspension I agree that a larger sway bar would work better. However, of all the improvements I made to my car, the one that made the most noticeable improvement was adding a Panhard bar to the rear. Granted that by the the time I added the Panhard I already had a very good front end system. Play with alignment settings to get the most out of your suspension. Try to get the most caster you can and get to at least 1 deg of negative camber. A little toe in doesn't hurt but keep it to the minimum like 1/16".
-Chassis improvements are also very important. Yes, I suggest subframe connectors and a good shock tower bracing (like a Monte Carlo bar). Once you start pushing the car around corners you want to control twisting with subframe connectors not only for stiffness but also to protect the 50+ year old unibody.
-A good seat belt, at least 3-point, should be a minimum. If you get serious about racing you will find that a nice bucket seat is necessary to keep you from sliding all over. If you are sliding all over the seat then it is one more thing you have to think about it when at a turn. A good dead pedal is great to push you back into the seat and control sliding.
-Tires. I don't know what tires you are running but there is a HUGE difference between typical radial tires and 200tw high performance tires. I don't know how much you will find for 14". I have 18" wheels and there is a lot to chose from. Tires are definitely the single item that will give you the most performance but to get there you can't skimp over what suggested above.
-Last but not least, once you have cover the above areas, it is seat time. Experience will make you a better driver. If it sounds overwhelming it doesn't hurt to start first with autocross and then jump to road racing. With autocross you can hone in your skills at much lower speeds and with less risks than road racing.
I am sure I am forgetting a few items but these are what first came to mind while responding. Please ask if you have questions.
