Paintbrushes come in may types sizes and prices. So how do you decide on a brush?
Material
Kolinsky Sable takes first place in brush hair. It is its ability to form a perfect point that makes it the most widely used brush hair by the most experienced miniature painters. Kolinsky Sable is very durable and has excellent paint holding ability. It holds a lot of paint and the paint does not come off until you want it to. (Compare that to a nylon brush which is too slippery and so the paint slides right off if you load it with paint.)
Sable, usually red Sable, has similar properties as Kolinsky but does not hold the same point. It makes a pretty good dry brush though as it holds paint well. Cheaper Red Sable with thicker hair will make a more durable dry brush than the better hair. Red Sable is cheap man's Kolinsky.
Squirrel is softer than Kolinsky or Red Sable and so it does not have the snap or stiffness that is needed for painting miniatures. It does, however, make a great dry brush.
Mongoose is very tough, affordable and holds paint quite well. Its durability makes it a wonderful dry brush that will just not die no matter what you do to it. A Kolinsky or Red Sable will eventually be destroyed by dry brushing unless it is a cheap Sable with thick hair. Mongoose brushes can make good points as well and are perfect for those who like a tough brush.
Synthetic or Nylon brushes really suck and in small sizes they offer only little savings as compared to a quality brush.
Shapes
From top to bottom; Bright, Filbert, Flat and finally Round.
I'll use the Bright and Flat styles for nearly interchangeable purposes such as large flat surfaces on vehicles or anything else I want to lay a smooth, even coat down.
I find that I never use Filbert tip brushes.
You will find yourself doing the majority of your work with Round Tips. They offer the most flexibility in uses, and the sharp points are great for detail work.
Size
A quality Kolinsky Sable brush will come to such a good point that a size 2 can have as sharp as a tip as a size 3/0, the larger brush will hold more paint and be bigger, but they both will have great tips. A size 0 and 1 is a good place to start. Then if you find that you liking the bigger brush better, you may want to add a size 2 at some point. If you find yourself liking the small brush better you may want to add a size 1/0, 2/0 or 3/0 at some point.
Most Recomended Brands
Raphael Series 8404 Kolinsky Red Sable
Windsor and Newton's Series 7
Dick Blick Sable brand (The cheaper alternitive)
You can find an in depth discussion on Raphael verses Series 7
Here
I agree with learning to clean your brushes. If you google brush cleaning you can find any number of video guides on how to do it.
As far as technique goes.......
Well there is to much to explain without knowing how advanced you are. There are several good guides both free and not floating around and I'll try to point you to some good ones.
Miniature Mentor One of the best tutorials out there. I suggest their first video. Its a bargin for the price.
Jereme Bonamant Teboul has a great video series but it is pricy. His site does have some interesting guides for free however.
Hot Lead What he lacks in natural talent he makes up for technical skills. He explains everything he does all the time and why. A decent buy, I would recommend Miniature mentor before this but its not bad.
Miniature Painting Secrets with Natalya A very long series with fairly bad reviews mainly because she tends to not explain very much. Its a good buy to see a master painter at work though.
Jen Haley's site has some great tutorials.
Figurepainters he has a very well written guide with a ton of pictures.
Ańa's blog
Painting Mum is a great read.
Chest of Colors Articles about everything from mold making, basing and painting. From beginner to expert.
Studiomcvey has some decent Youtube tutorials, although these are geared more for the beginner.
Crooked eye studios has some tutorials although they are a bit sparse on information and a very nice gallery.
Destroyer Minis has a quick and easy tutorial on painting eyes.
Jrn has several guides.
Lost in the warp has a great deal of tutorials but they are kind of hit and miss. Still its not a bad idea to browse through it.
Akaranseth has yet more tutorials, some are on painting but most are on terrain.
Anyway I hope that helped. I can add more later if you need some or if you are looking for anything in specific. Just let me know.