I have now beaten the game with four builds using these strategies. They were:
Pistol Build - Take One Hander and Gifted. Uses both .223 Pistol and Alien Blaster as endgame weapons. .223 Pistol is used for longer range and alien blaster for closer range and tougher foes. In Fallout 2, I used the alien blaster together with the Gauss Pistol. The Gauss pistol was used for longer range and the alien blaster against tougher foes. This was the only build where I was able to successfully take out Horrigan without having to resort to using the turrets against them, but then again, I was just lucky.
Sniper - Uses the Sniper rifle and the Turbo Plasma Rifle in Fallout 1, and the Gauss Rifle together with the Pulse Rifle in Fallout 2. Both used Gifted and Small Frame.
Energy Burst Build - Used the Gatling Laser, with the .223 Pistol for weaker foes and conserving ammo in the first game, and the Gauss Pistol in the second game for the same reasons. Both ranks of bonus ranged damage were taken. Gifted and Fast Shot were the perks.
Big Guns - Gifted and Fast Shot were my traits. The Minigun and .223 Pistol were used together. Both ranks of bonus ranged damage were taken. I also used the rocket launcher to take out clusters of tougher enemies at one. In the second game, I used the Bozar and the Gauss Pistol. Later I got the Vindicator minigun.
Now I've got some new ideas and will remake all these characters, having two different builds, one for both genders, except maybe the pistol build because there aren't very many great pistols in fallout 1, only the .223 and the alien blaster, though in fallout 2 there is the Gauss Pistol and the Pulse Pistol, so basically there is no variation to this build.
Now for the other builds, this is what I have planned.
Sniper - In Fallout 1, use the .223 Pistol and the Sniper Rifle if using only small guns. If switching to energy weapons, use the Turbo Plasma rifle and the .223 Pistol. In Fallout 2, use the Gauss Rifle with the .223 Pistol if using small guns, or the Pulse Rifle and the Pulse Pistol if switching to energy weapons later. The .223 Pistol will be used as a backup weapon in case I run into enemies with a high pulse resistance such as floaters.
Non Big Gun Burst Fire - Take both ranks of bonus ranged damage with the fast shot perk. If using only small guns I'll use the .223 Pistol and the Assault Rifle in Fallout 1, and the Gauss Pistol and H&K G11E in Fallout 2. If switching to energy weapons, use the Gatling laser together with the .223 Pistol in Fallout 1 and the Gauss Pistol in Fallout 2.
Big Gun Burst Fire - Take fast shot as a trait. Now I need to choose whether to use the machine guns or flamethrowers. If using machine guns, take both ranks of bonus ranged damage and use the minigun together with the .223 Pistol in the first game, and either the Bozar or the Vindicator Minigun with the Gauss Pistol in Fallout 2. If using Flamethrowers, use the flamer together with the .223 Pistol in Fallout 1, then use the improved flamer loaded with mark II fuel in fallout 2 together with the Gauss pistol. Be sure to take the pyromaniac perk.
I haven't tried going through the games with either a melee character using what I've learned from advice on this thread, or a dimwit. But I think with a melee character, I'll need to use diplomacy to get through most situations and avoid most of the combat due to most of my enemies using guns. Either that or I'll need to develop a secondary combat skill or command my npcs to do so. And what would be the best way to develop a dimwit? Maybe that's a topic worth a new thread?