Hi OP, I'm an MUA and have all sorts of high end and cheaper brushes in my kit. What I'd recommend depends on the type of finish you want (full - sparse coverage, dewy, matte or semi matte). There's nothing wrong with applying with fingers as long as they are clean to start with, some products do work better with the warmth of the fingertips. Here's what I'd use;
Synthetic hair, densely packed brushes are better generally for more full coverage, matte finishes. They also don't absorb as much product. Apply in a buffing motion so no streaks. The real techniques brushes or Primark are good for cheap, bdellium and sigma are good for high end.
If you want a more dewy, natural finish I'd go for a moistened beauty sponge (put it under the tap so that it grows in size and then squeeze the excess water out so it no longer drips) and apply in a sweeping/dabbing motion. Real techniques miracle sponge for cheap, beauty blender for more high end.
The above would be for cream or liquid based foundation and concealer. If using a powder either use a dry sponge for full coverage or a fluffy brush for build-able.
Sorry for the long post but without knowing your skin or the products you're using its easier to give an overviews to cover all bases. Also, wash brushes every 3-4 uses ideally to keep them clean and working to their best capacity (I recommend baby shampoo).