Hi!
I agree that flat-soled, flexible shoes are the way to go, and throughout most periods I believe such shoes were what the fighting men used when they trained.
With that said, I'd just like to add that it is also important to study a bit the footwear fashion apart from the martial arts context, as the men needed to be able to use their skills in whatever they happened to be wearing. And the shoes you had when riding, for example, may have had completely different requirements.
These are later period, but for example Petter and Porath both show men fighting with heels, so in case these periods are "your thing", it would be best to be able to fight also in fashion footwear.
Yours,
Ilkka