Sunbeam is a classic English brand, long gone from the market and remembered by only a handful of enthusiasts. But the Alpine is a nice-looking car with reliable and conventional mechanicals. Also, it comes with a small 1.5 or 1.7-liter four-cylinder motor. Over the years, Sunbeam built over 60,000 Alpine roadsters, so finding one is easy. For under $20,000, you can find an excellent example of this exciting car (via Supercars).
However, if you are looking for a more serious machine, look for the Sunbeam Tiger. This model seems identical to the Alpine but packs a 260 or 289 Ford V8 engine under the hood. That gives it a much better performance and soundtrack. However, it still needs to be exhilarating. But best of all, the legendary Carroll Shelby designed this model before he worked for Ford.