For mineral base (foundation) two kinds of brushes are recommnended: Kabuki and Flat Top.
Flat top has a flat top. The handle may be short or long:
image from Cream89
Kabuki looks a bit like your dad´s shaving brush: it´s rounded:
image from ayako
Which to choose?
Flat Top gives a heavier coverage and the Kabuki gives a lighter one. Some people love one, some the other, so there is no definite winner here.
Also, the more compact the brush is, the more coverage it will give. In less compact brushes the bristles "open" more, giving lesser coverage.
The Flat Top can "swallow" up a lot of powder and give you too much coverage. The trick to avoid this is to put a teeeny bit of mineral powder into a lid / bowl, swirl the brush in it a couple of times, and tap off the excess. This way the brush is evenly coated, and cannot take too much powder.
The Kabuki gives a lighter effect, so if you want more coverage you will have to do several layers. It is also great for finishing powders.
If you have a chance, test these two kinds of brushes and see what you like best. I chose the Kabuki because I prefer a lighter coverage. But I ended up also taking light-coverage foundation powder (Cashmere and Luminesse from Lumiere) and I usually have to do 2-3 layers before I get the coverage I want. I suspect that with the Flat top I would need to do just one layer. But I'm happy with the control I get with the Kabuki: I prefer too few foundation than too much.