Having built a few kit cars and sand rails - including converting one to a "street car" - I can add my opinions.
Almost all kit cars were not well engineered, designed, nor manufactured. They require a TON of modification and alteration to even get close to making them work. And the cost escalates VERY quickly due to the multitude of additional parts that are needed to complete them. Especially when you consider the final result never seems to be what you envisioned. To me it is one of those things where the allure of the concept far exceeds the reality of it.
Sand rails have suspensions designed for off road applications. Even with plenty of modifications they tend to not handle well on the street. Particularly if you intend it to be a performance vehicle rather than a dual-use one (on and off road).
My preference would be to find a vehicle with a overall style that you love, with a decent condition body, then completely replace the entire undercarriage (chassis, suspension, powertrain, brakes, etc) with components from a higher performance vehicle. Either a total "body swap" or a extensive components swap. Making it look like a classic vintage car but with the performance and functionality of a modern one. As Karl said, that Multipla would be fun. A few years ago I had the opportunity to get one with a very solid body shell, but rusted pans and missing most of the mechanicals....with the intent to do a complete swap. However I passed due to a lack of time to add yet another project to my list.
Some other models that I'd love to build include a Autobianchi A112, or a Fiat 127 / Panda / Uno, or a Yugo, or a Lada Niva, etc...body swapped and slammed to the ground with tons of customization.