When you level up, you get one point to spend on a perk, and five points to use on weapon skills. While the points may not do much early on, they add up in a hurry! Then there's that infernal question... what are you going to boost? This is a detailed breakdown of what you get for boosting each area.

Note that all areas (save the healing skill) boost minimum and maximum damage, so those stats are omitted.

Melee: Accuracy
Pistols: Accuracy
Shotguns: Accuracy
SMGs: Accuracy
Assault Rifles Accuracy
Sniper Rifles Accuracy, Minimum Range
Grenades: Dispersion (Accuracy)
Rocket Launchers: Dispersion (Accuracy), Minimum Range
Heavy Guns: Accuracy, Minimum Range, Increased Minimum Damage boost
Traps: Increased Damage boost
Healing: Healing Power of Medi-Kits

Also, boosting skills will change your starting weapon when you start a game with no items!

(* indicates a secondary weapon. You can start with one primary and several secondary weapons.)