I have SO many opinions on this topic so get ready :). Coming from a makeup artistry background I am biased to being a major brush fan and wanting to have options. Having done countless one-on-one lessons with women and having met them during our Green Beauty Workshops I can tell you that most ladies are skimping on the brush front. They'll drop $50 for a foundation (that will expire in a year mind you) but balk at spending the same on a brush that will last them years. YEARS.
Good brushes allow you to apply your makeup effectively and honestly helps your makeup stay on longer. Oils from your fingers break down makeup and I'm not even going to talk about having to work literal magic to get that little sponge tip applicator to do anything other than make your eyeshadow look like a stripe. Same goes for the teeny blush brush that may come with your blush. And if you're feeling some pride in the fact that you make those tools work (some of which are really meant to be single use) then IMAGINE WHAT YOU COULD DO WITH A BRUSH!
So assuming you're on board, let's talk hair - you can either do natural or synthetic. Natural is the umbrella that sable (which is actually an animal called a sable), badger, squirrel, goat, pony, or weasel (which is a less cool sable), amongst a few others, fall under. Synthetic brushes are cruelty-free as they don't entail harvesting any fibers from animals and are known for being super soft. They also don't aggravate sensitive skin nor do they absorb your products the way natural brush fibers do. As a result we use synthetic taklon for almost all of our brushes.
CARE - for natural brushes I rec shampooing and conditioning. Synthetic brushes can be cleaned with dish soap. This post talks all about the how-to of cleaning brushes. Do you need to buy a brush cleaner? I think they're good if you aren't good at washing your brushes or you're a makeup artist and have to clean colors/sanitize brushes in between people. Otherwise I think you're fine just washing them. How often should you do it? Once a week is ideal but few people do it so aim for once a month. If you have an "open" breakout I would wash the brush that night so as to not transfer bacteria.
LIFETIME - generally speaking you get what you pay for. I find individual bushes tend to be better quality over brush sets. I also find synthetic brushes don't shed the same way that natural fiber brushes do. A good brush should last you at least 5 years and can last 10-15 if you're nice to them. You may have to reglue the ferrule (the metal part) if it detaches after years of use but grab your glue gun and, voila!, new brush.
Here's how I use each one in my kit:
FOUNDATION BRUSH: There are two camps in foundation tool applicators - brushes and sponges. I fall into the brush camp. I used to work for a makeup company that had a $58 foundation brush. I LOVED it as it gave an airbrushed finish but I found that the hairs were too long for my liking and I would always pinch it so I would get a little less loosey goosey, a little more firm application. When I chose the Foundation Brush for Erin's Faces I chose a brush that I didn't have to pinch but still gave me the finish I wanted with foundation - it makes it look airbrushed into skin. AND I wanted it to be cheaper so I priced our Foundation Brush at $25 - it applies primers, tinted moisturizers, BB/CC creams and foundations beautifully.
POWDER BRUSH: This is a must-have, non-negotiable in my book. I use it to apply powder of course, but also to blend blush out (with an empty powder brush) or get a diffused bronzer look - it is a major workhorse and worth investing in a good one.
BLUSH BRUSH: As we've discussed, if you are using the little scrawny brush that came in your blush compact please be a grown up and pitch it. That thing is too small to do a good job unless you are a genie. I really love an angled head on a blush brush because it makes your blush application pretty fool-proof - just pop on the apples, blend and go.
EYESHADOW BRUSH: These are like jeans - everyone likes a different kind but in my opinion you need at least two: one to put your shadow on and one to blend it. The "putter on'er" can be pretty basic - I like this one from Root Pretty- and the blender brush will have to be flexible but balance firmness. I was raised as a makeup artist on Urban Decay brushes as they were the first line I ever worked for so I'm partial to their blender brush.
Then we get into brushes that you may or may not need depending on what you're doing:
EYELINER BRUSH: Necessary if you use a pot/cream/gel eyeliner. And, in my opinion, you should stick with a synthetic one here as natural brushes fray far more quickly and you want a tight line for this brush. This is also a "shorter lived" brush as you've got about 2 years to use these if you use them 5 or so days a week - you're doing such specific work and eventually the brush will fray/open up but you get a longer timeline with a synthetic one. These also get gunky so washing after every few uses or keeping a spray bottle with alcohol on hand to break through that eyeliner build up is key.
HIGHLIGHTER BRUSH: This is the only area where I'm still using a natural brush. Thus far I haven't gotten the subtle payoff from synthetic brushes - they pick up more pigment than I want so we use tanuki hair. You want something that gives you control and isn't too big.
CHEEK CONTOUR BRUSH: Please, please, please don't use your blush or powder brush to contour your cheeks - they're both generally too large and one is full of pink blush which you're not going to get out adequately if you just used it to apply blush. For this genre you want a thinner brush that allows you to carve out your cheekbones. I generally then blend it out with an empty powder brush.
Let us know if you have any questions!