Lithium batteries would definitely be more cost effective in the long run. However, they are a lot more expensive up front. They're also finicky, so you will want some sort of battery management system (this is what OEMs do), or you'll have to keep a very close eye on them (which I've found isn't so easy).
Motors are mostly whatever you prefer or can find. I am not exactly sure how you use a floor burnishing machine. Do you need RPM control, or is it just on/off? I would imagine that a permanent magnet motor would be a good fit though. That is what I'm using on my electric riding mower, and they aren't too pricey either. Mine is made by
motenergy.