When upgrading your weapons you can improve the following categories:

Body: Increase damage and range.
Clip: Faster reload speed and bigger clip size.
Sights: Allows you to zoom in and get accurate shots.

Because of the cost of upgrading, it is best to choose one weapon and maximize all of its upgrades. Start by upgrading Sights first, then make Clip the next priority. Save Body upgrades for last. By following that order you can get the best performance as early possible. However, do not maximize one type of upgrade and totally ignore the other two. Make sure you allow the other upgrades to progress if the weapon's performance is beginning to suffer.