I had a '66 for about 5 years. It was fun to zoom around town in, but I never put the time or effort into making it reliable enough to trust it. It was sort of like the Harley of vehicles: spend 3 hours working on it for every 1 hour driving it.
In stock form, the unpowered drum brakes were hazardous, and ditto the manual steering, so plan on upgrading both of those. The stock gas tank was 12 gallons- good for around 100 miles with the carb'ed V8, but 22 gal replacement tanks are available. Nothing major ever broke on mine, but it suffered from old-truck-itis- everything rattled leaked and squeaked.
It was fun when I was 20, less so when I was 25, and I sold it when I was around 27. I rarely miss it.