I have badger, boar and synthetic brushes. They all function equally well with soaps, croaps and creams.
Sam, I'd recommend an inexpensive but great performing synthetic brush, under $15. I would strongly recommend that you stick with one set, razor, soap, brush and do this for 30 days.
Have you considered horse hair brushes? After hearing rave reviews about the Vie Long, I bought one of their Epsilon Model GC13900/3 brushes. It has cloud soft tips, yet plenty of backbone. It works great on soaps, creams, both mug lathering and face lathering. Here is the review I did of it, in case that helps. Currently selling for 43.75 Euros, that is still only $52.12 for a fantastic brush. Here is the Gifts & Care website with the brush. Just search for "GC13900/3" on the page and you will find it. Gifts & Care is in Spain, but their shipping is fast and their customer service excellent.