Brushes can be confusing at times, and complicated too. Selection of material and sizes vary wildly.
Broadly speaking, a larger brush offers more coverage while a smaller brush offers more control. If you opt for small knots (under 22 mm) you should go for short lofts, and conversely if you want to use a big knot (over 22mm) you should choose a tall loft.
Personally I like my brushes on the small side, with a knot around 19-20 mm across and 55-60 mm tall loft. However, in my opinion this size is best suited for horsehair and badger with a lot of backbone. A softer badger should be larger, say a 22-25mm knot with a loft between 60 and 65 mm tall. Boar brushes also work well in large sizes, but I have used small boars that work just fine.
As far as the hair go, that is complicated too.
Avoid the so called “pure” badger if you want a high end brush; this is in fact the lowest grade. Opt for “fine” or “silvertip” if you can, since they are both softer, retains water more easily and also lathers much faster – but be aware that thee is no set standard for what constitutes “pure”, “fine”, “silvertip”, or any other grade. Ask around or check the manufacturers website to work it out.
Boar hair are not graded, but I would avoid boar that is dyed to look like badger; this is often perceived as wearing faster due to the dye. A good boar will have tips that split during use and softens with age.
Horsehair is somewhat of an acquired taste, people either love or loath it. I’m a fan of a good horse brush myself, but I do admit that I’m a minority in that regard. Horsehair brushes are made from a mix of mane and tail hair, collected during normal grooming. More tail means a stiffer brush with more backbone and more scritch. For those who care, it’s the only animal hair I know of used for shave brushes that is collected in an animal-friendly way.
Synthetics varies wildly, so it’s hard to generalise about those. My experience with them is also limited to cheap ones from a decade or two back… and synths have come a long way since then.