I would suggest going to
r/wicked_edge/ on reddit. List a specific price range and you will be flooded with suggestions.
A little break down for you. Badger bristle brushes are generally regarded as the softest. They are usually broken down into 4 grades of quality, pure, best, super, and silvertip. They generally get softer and possess better lathering qualities as you go up the scale, and the price climbs accordingly.
Boar bristle brushes are also used by many. Some even prefer them. They are generally "stiffer" than badger but help lathering off of hard soaps etc.
Horse hair brushes are also revered by some. They generally are described as a hybrid between a badger and boar in regards to how the feel/lather.
Synthetic brushes are also a viable option. Many are well respected by wet shavers.
In regards to finding a "quality" brush for cheap, boar or synthetic is probably your best best. If I had to grade cost/quality it would be boar,synthetic,horse,badger. Badger are nice, but to get the higher quality you are spending a lot of money ($50-100). You can get a respected omega boar brush for $10-15. But the bottom line it will be extremely difficult getting anything worth shaving with for a few dollars.
Scan through this thread
thread. to get suggestions.
This horse hair brush was the cheapest, well reviewed one I could find.
Hope this helps!