You could always buy a second hand tank and filter, although you'd have to clean them very well. That's almost always less expensive then buying a brand new set. And yes separators work but the betta's can still usually see each other and that causes stress and agression. Also it messes with filtration so I suppose one side would be less filtered than the other unless you plan on putting a filter on either side of separator. Wouldn't recommend it though in general. I'd just say go for a five gallon separate tank for each betta you own if you want more than one instead of having a separator in a ten gallon. But honestly personal opinion so feel free to do that, good luck though
