Part of good makeup is having the proper tools: good brushes. And by "good brushes", I most certainly don't mean that you need to spend a lot of money on them. Some of my favorite brushes are a few dollars. With these tools, it will really be often a matter of preference in terms of what you like best for which application.
Back before I started on my quest for good makeup, I was sometimes stopping myself from using certain brushes because I didn't know what they were for. Well, that's just silly. The manufacturer may have stamped a name to a brush, indicating what it should be used for but, really, there is no "brush police" that will come give you a fine if you aren't using the brush exactly as intended. The only "sin" here is to not use the brushes.
Brushes sets
Again, even before the quest for good makeup, I had invested in a makeup brush set akin to this picture. If you do a search on eBay for "makeup brush set", you'll see plenty of these kinds of sets. The quality of the brushes is okay but you can get these for a very decent price (32 pieces for 10-20$ including shipping). A lot of the vendors will be in China and, actually, often these brushes are very akin to the higher end brushes. One thing is that they tend to shed their bristles for a bit but then it stops. It's definitely one way to get plenty of brushes for not too much money up front. And then you can subsequently replace your favorite brushes with higher quality brushes. That's definitely what I did: I used the kit for many many years and I still use some of those brushes every now and then.
That being said, there are now a lot of options to get brushes at decent prices, so look around and you will likely find something that will fit in your budget.
My favorite brushes
Now onto my favorite brushes and what I use them for. I use these on a near daily basis... if not daily, it's on a weekly basis for sure.
Sephora Pro Natural Small Eyeshadow Brush - Sold out
Unfortunately this brush is sold out but I love it and use it very frequently. It is stiffer than the one above so I love to use it to apply creamy eye shadows. So, whenever I apply the Buxom Stay There shadows, I use this brush.
e.l.f. Professional Eyeshadow Brush - 1$
I love this brush to apply loose powders eye shadows or glitter over the eyelid. It is a rather stiff brush so it's great for these applications. It does well also for regular pressed powders.
Sephora Pro Smoky Liner Brush - 17$
(note that it's not exactly the brush that I purchased but the same shape and it's the same brand) I love this brush to apply gel or cream eyeliner. I somehow prefer to use it for a stage makeup application but it can be used for any eyeliner application. The shape of it is what makes it so great: it is akin to working with a pencil eyeliner.
MAC Small Angle Brush - 19$
I use this brush to apply either cream or gel eyeliner and to do my eyebrows. I generally will use this brush for my regular makeup. I've had this specific brush for like over 15 years and it's still going strong with no signs of decline.
e.l.f. Contour Brush - 3$
Sephora Classic Rounded Crease Brush - 17$
This is similar to the e.l.f. Contour Brush in that I use it to apply eye shadows at the crease of my eyes. However, this one is fluffier and, as such, will automatically blend in the color a bit more. For regular makeup, that is generally what I want (but not always). For stage makeup, that's too much blending.
Sephora Pro Allover Shadow Brush - 20$
e.l.f. Studio Blush Brush - 3$
I love to use this brush, as the name indicates to apply blush to my cheeks. It is the perfect size for me. I have encountered many blush brushes that are either too large or too small. This one's perfect for my cheeks.
e.l.f. Complexion Brush - 3$
I use this brush to apply loose powder to my face over my foundation. It has the perfect size and shape for it.