Really you just have to use some of the same tricks that you'd use for a speed-run... stealth, diplomacy, and lots of reverse-pickpocketed explosives. If you don't care about saving and reloading in combat, it doesn't really matter that much honestly. If you don't like doing that, then you just need to be very careful when fighting against people with miniguns or rocket launchers. Combat and Brotherhood armor are extremely effective against pretty much all of the other weapons except for flamers, but flamers have such a short range that they generally aren't a huge issue. Being a sniper-type character really really helps with all of that, though. I always like using the Alien Blaster for the damage and AP values, but it's only really viable if you have power armor. Stick with the Turbo Plasma Rifle or .223 pistol. (Also note that thrown flares will cause serious damage to characters in Power Armor, if you want to fight the BoS guys. Try it sometime.)
For endgame stuff, you can talk the Master down without a fight if you know about the sterility, you can surrender Harry in Necropolis and talk to the Lieutenant and still escape with all your gear, or you can infiltrate the base normally and blow it up without ever setting off the alarm if you're sneaky enough. While power armor is very useful, there's only a couple of places where it's really necessary for survival, and in those places fights are generally optional, or can be won with trickery instead of strength.
