The bristle of choice on a shaving brush is badger hair. There are different grades of badger brushes that cover the quality of hair selection. A "pure badger" brush is the lowest of these grades. The top grade is the "silvertip". These things can be pricey. Perhaps one day I will move onto a finer brush, but for now I am content with my brush, which I believe is pure badger.
I would advise against trying to save money and buy a boar shaving brush. I had one back when I didn't know better. The bristles were very stiff and I didn't have good shaving results with it. The bristles were just too course and didn't seem to apply the soap well. Besides would you rather behold a badger (even if it isn't this kind) brush or a boar brush?
Not only does the brush feel nice as you apply the lather to your face, it actually exfoliates a bit. This prepares your whiskers and helps produce a better shave. The brush is great for causing hairs to be softened and raised up away from the skin. The razor can then glide across the skin and cut these raised hairs easier than if a shaving cream was applied by hand. And it does feel luxurious and some times refreshing to lather on a nice soap to your face!