I have a dedicated brush for every soap, but I prefer boar brushes and they don't cost much.
I rotate through my soaps each shave so my brushes end up drying for a few quite a while before their turn comes around again.
I never wash my brushes in shampoo or anything like that, they get a good soaping while I use them and then a good rinse so that's good enough for me, also the reason I use dedicated brushes is so that each brush smells like the soap it's earmarked for and I like it like that.