One of the first considerations for a cosmetics brush is the material. There are many with nylon or other synthetic materials for the bristles, and those can be great. You can also get some that are made out of soft, natural materials that work very well. It is a personal choice. However, when you do buy a brush, you want to spend some money to get a nice one. The cheaper ones usually scratch your face, have handles that fall off, and won't last very long in general. You don't want to keep buying them. Get a good one from the onset.
Once you find a decent one, you can then see what it can do for you. You should always have a nice one that you can use to apply both powder and blush. These are on the larger size. You should always have one with a cap of some sort to keep dust out. When it comes to your eyes, you have to have a smaller cosmetics brush that will sweep your lid and above your lid without putting shadow where you do not want it to go. You can get a very thin one to work in the crease of your eye, if you apply your makeup that way, and that can also be used to apply other small areas of color.
When you first use a good brush, you should know a few things are going to happen. One thing is that your brush or brushes are going to lose bristles as they go. The larger ones are going to do this more often, but the smaller ones can do it as well. They should not lose a lot, but they are going to lose a few. It's no big deal. You should also know that they are going to work best if you keep them away from the toilet area of your bathroom. The last thing you want is germs splashing up on them, and those germs can fly around the room further than you think.
You must also take care to keep your favorite cosmetics brush clean. Once a week you should use mild soap and water to thoroughly clean out your brushes. They are going to be full of makeup and dead skin cells, and you want to get that stuff out. Make sure you run it under cool water until all of the soap runs out and the water is clear. Let them dry. Good ones will take this well and can last you as long as you take care with them.