What would be the best type for Smart Robes? HP? Def? Spirit?
That depends on your needs. Need more defense? Go for Shield type, need more spirit? Go for Barrier type.
Vital i would avoid as while it gives 144 more hp than Barrier and Shield types it has way lower defense and spirit, making it not worth it in my humble opinion.
I would however say that Barrier is the best type for Smart Coat for it's huge spirit versus other types.