It's never going to feel as composed as your S3, or any other similar modern car for that matter, but replacing suspension components with as new equivalents will make the world of difference. If the tyres are as old as you say, the chances are many other wearable parts on the car are much older, so will be getting tired.
VW Heritage do a very good range of OEM or as good as products, so I'd use them as a benchmark for what parts are available and prices.