Professional makeup brushes?

Hi guys. I was wondering if anyone can tell me what brushes I should have in my kit for professional makeup artistry. I'm really passionate about makeup, I love testing new products and trying new looks just for fun and I am applying to cosmetology schools this year. I have an assortment of makeup for all different types of skin tones and I know the importance of keeping my brushes clean (even if I do say so myself, I do a really good job cleaning and taking care of them). As it stands right now, I have the following brushes/tools that I use:

.Eyeshadow brush (two different sizes)

.A smudging eye sponge

.Lip brush (again, two different sizes)

.A foundation brush

.Blush brush (three different sizes)

.Bronzing brush

.Cosmetic sponges

.Powder puffs

.Eyebrow brush/comb

I'm planning to buy an all over face brush today. Are there any other brushes I should seriously look into purchasing? And if so how necessary are they to a kit? Thank you for your time :)