You should select a brush based on the type of paint you are using, as well as the area that you will be painting, and how much control and precision you need.
Natural-bristle brushes are made with animal hair. They are used for applying oil-based paints, varnishes and other oil-based finishes. The bristles have natural split ends that hold more paint and provide for a smooth finish.
Synthetic brushes are easy to clean and work well with all types of latex paints. Higher quality brushes will be a blend of nylon and polyester providing durability and excellent shape-retention. They are also available in polyester only.
Brushes are available in a wide variety of sizes. Much depends on your comfort level and preference, but here are some general rules of thumb:
Chisel - slanted bristles produce a straight line, good for trimming in corners and edges