1. Sunbeam Tiger
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 dependable 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 a nice example of this interesting car (via Top Speed).
However, if you are looking for a more serious machine, you might want to look for the Sunbeam Tiger. This model looks identical to the Alpine but packs a 260 or 289 Ford V8 engine under the hood. And that gives it much better performance and soundtrack. However, still not exhilarating. But best of all, the legendary Carroll Shelby designed this model before he worked for Ford.