First, please read my post about a basic watercolor set where you can find information about brushes for beginners.
You can see many types of brushes in art supplies stores.
First, not all brushes suit to watercolor painting.
Second, you need a few different brushes for watercolor painting.
When you paint with watercolor you do different kinds of work in one painting:
Wash is a layer of color(s) with diluted paint. For this kind of work you should have a soft brush which absorb diluted paint very well and give away the paint on a paper surface.
Classical brushes for washes made from natural hair. I use a round squirrel brush.
However you can find soft synthetic brushes at stores. It's a good idea to test them.
2. Structures and stripes
If you paint architectural elements, man made structures, straight stripes or lines you should have flat brushes. It's easy to create rectangular shapes with them.
Again it's better to have flat brushes made from natural hair too.
3. Fine lines
When you create fine lines you should have a fine brush usually with a round shape,
ideally made from natural hair. I use a sable brush.
You can create nice fine lines with your round squirrel brush too because it has a sharp point which is very important for painting.
When you do strokes big or small, short or long you can use all types of brushes.
Natural hair round brushes has the ability to be molded into a variety of forms.
What size should I buy?
First, all brands have their own metric system.
Second, it depends on your paper size.
If you do small sketches let's say 5x8" you do not need big brushes. Round squirrel brush for washes 8 mm in diameter may be too big because it give away too much diluted paint and it can be too wet.
If you paint 9x12" size this kind of brush suits very well.
If you paint bigger format you should have bigger brushes more than 1cm in diameter.
You should have at least 2-3 brushes for watercolor painting - different size and shape, ideally made from natural hair. They are not cheap however they last long life and it's easy to wash them and care about them.
In the meantime, watch my video with a quick watercolor sketch and stay tuned for a tutorial: