DwayneGAnd
Look, Ma! Two Heads!

Thanks to all my research on the Fallout wikia, I have come up with builds that use what I believe work to maximum effect. Feel free to comment on my conclusions.
Fallout 1
Small Guns- Use the .223 pistol. According to the Fallout wikia, the .223 pistol has a unique weapon penetrate perk which allows it to ignore 80% of your enemies damage resistance. It's also the only gun in the game with this perk and only one of three weapons to have this perk. For enemies a further distance away, use the sniper rifle.
Energy Weapons- Use the alien blaster, the single best pistol in the game. This weapon comes with a unique weapon accurate perk with gives it a bonus of 20% accuracy over over weapons. In fact, any build using the fast shot perk can use this weapon to quickly kill deathclaws at very close range, even with minimal investment in Energy weapons skill. Your long range weapon depends on whether or not you take the Fast Shot trait. If you do not, use the Turbo Plasma Rifle as it's the best long range weapon in the game. If you do take Fast Shot, use the Gatling Laser and get Bonus Ranged Damage. With the Sniper perk and a Luck of 10, every shot will be a critical hit, allowing you to penetrate armor.
Big Guns- Since Big Guns don't appear until much later in the game and are more efficient as a secondary combat skill, use small guns as your primary attack skill. Use the .223 Pistol to conserve ammo and the Minigun to decimate tougher foes with Sniper and a luck of 10. Fast Shot is the best trait because burst shots cannot be aimed and all big guns use only burst fire, even the flamer and rocket launcher.
Melee- Use the Power Fist or the Ripper. Both also have the unique weapon penetrate perk.
Fallout 2
Small Guns- Use the .223 Pistol for the weapon penetrate perk. Though the Needler Pistol is the only other gun in the small guns category to have this perk, the .223 pistol deals more damage and its ammo is more common. For longer ranges, use the Gauss Rifle.
Energy Weapons- Same as above, but if not using Fast Shot, use the Pulse Rifle. Use the Pulse Pistol until you can get your hands on an Alien Blaster. Living Anatomy is better for single shot weapons. Take Bonus Ranged Damage if using the Gatling Laser. Both pulse weapons have the weapon penetrate perk.
Big Guns- Take Fast Shot. Again, big guns don't appear until much later, though there are more to choose from in this game. Your best choice is the Bozar, which when combined with Bonus Ranged Damage, Sniper, and a luck of 10, makes for a deadly combination. That and its ammo is extremely common. Since you use Fast Shot, use the Gauss Pistol for taking out weaker enemies to conserve ammo and to take advantage of its low AP cost.
Melee-Use the Mega Power Fist or the Ripper to take advantage of the weapon penetrate perk these weapons have.
Fallout 1
Small Guns- Use the .223 pistol. According to the Fallout wikia, the .223 pistol has a unique weapon penetrate perk which allows it to ignore 80% of your enemies damage resistance. It's also the only gun in the game with this perk and only one of three weapons to have this perk. For enemies a further distance away, use the sniper rifle.
Energy Weapons- Use the alien blaster, the single best pistol in the game. This weapon comes with a unique weapon accurate perk with gives it a bonus of 20% accuracy over over weapons. In fact, any build using the fast shot perk can use this weapon to quickly kill deathclaws at very close range, even with minimal investment in Energy weapons skill. Your long range weapon depends on whether or not you take the Fast Shot trait. If you do not, use the Turbo Plasma Rifle as it's the best long range weapon in the game. If you do take Fast Shot, use the Gatling Laser and get Bonus Ranged Damage. With the Sniper perk and a Luck of 10, every shot will be a critical hit, allowing you to penetrate armor.
Big Guns- Since Big Guns don't appear until much later in the game and are more efficient as a secondary combat skill, use small guns as your primary attack skill. Use the .223 Pistol to conserve ammo and the Minigun to decimate tougher foes with Sniper and a luck of 10. Fast Shot is the best trait because burst shots cannot be aimed and all big guns use only burst fire, even the flamer and rocket launcher.
Melee- Use the Power Fist or the Ripper. Both also have the unique weapon penetrate perk.
Fallout 2
Small Guns- Use the .223 Pistol for the weapon penetrate perk. Though the Needler Pistol is the only other gun in the small guns category to have this perk, the .223 pistol deals more damage and its ammo is more common. For longer ranges, use the Gauss Rifle.
Energy Weapons- Same as above, but if not using Fast Shot, use the Pulse Rifle. Use the Pulse Pistol until you can get your hands on an Alien Blaster. Living Anatomy is better for single shot weapons. Take Bonus Ranged Damage if using the Gatling Laser. Both pulse weapons have the weapon penetrate perk.
Big Guns- Take Fast Shot. Again, big guns don't appear until much later, though there are more to choose from in this game. Your best choice is the Bozar, which when combined with Bonus Ranged Damage, Sniper, and a luck of 10, makes for a deadly combination. That and its ammo is extremely common. Since you use Fast Shot, use the Gauss Pistol for taking out weaker enemies to conserve ammo and to take advantage of its low AP cost.
Melee-Use the Mega Power Fist or the Ripper to take advantage of the weapon penetrate perk these weapons have.