High Agility. That is the base SPECIAL score for Action Points.
Traits are optional, but the Kamikaze trait will give you a +10 AP bonus. It will also cost you 2 points from your DT for being so reckless. Once a trait is taken, you can't get rid of it later unless you cheat.
Tagging the gun skill you plan to use most will raise you skill and your accuracy in VATS.
Raise the SPECIAL score related to your favored weapon type; Agility for Guns, Perception for Energy Weapons. This also increases your accuracy.
VERY IMPORTANT: Find weapons with a very low Action Point cost. Here are some examples.
GUNS: .357 magnum revolver (20 AP), 10mm pistol (17 AP), 10mm SMG (20 AP), 12.7mm pistol (17 AP), 12.7 mm SMG (20 AP), 9mm pistol (17 AP), Assault Carbine (20 AP), Cowboy repeater (20 AP), Marksman carbine (20 AP), Silenced .22 pistol (17 AP), Silenced .22 SMG (18 AP). As points of comparison, the gun with the lowest AP cost is Benny's "Maria" 9mm pistol (15 AP) and the highest is the Anti-Materiel rifle (65 AP). My personal favorite vanilla pistol is the "Lucky" .357 magnum revolver (17 AP). With handload ammo that gun kicks ass. The Cowboy perk also applies to that gun. The 12.7mm SMG hits hard and fires 3 shots for every burst (20 AP) in VATS. It's great against Cazadores in VATS.
ENERGY WEAPONS: Alien Blaster (20 AP), Laser pistol (15 AP), Laser RCW (20 AP), Laser Rifle (18 AP), Plasma defender (20 AP), Recharger pistol (13 AP), Recharger rifle (19 AP). The Energy Weapons with the highest AP cost are the Flamer, Incinerator, Heavy Incineragtor, and Euclid's C-Finder (all 50 AP).
Note that some of these weapons don't do much damage. The "Recharger" energy weapons have a low AP cost, but have a recharge time to be taken into account. They cannot be "reloaded" at any time of your choosing like other weapons.
Happy hunting!