GUNS: For most work, I'm pretty partial to the Cowboy Repeater, but I've only played through the game a few times. When I begin the final assault on the Legion, I switch to the Assault Carbine with armor-piercing rounds.
ENERGY WEAPONS: Never had EW as my primary weapons of choice. I did heavily use an Incinerator for targets with a high DT, the flames did what the attacks themselves did not. Took down all of House's penthouse securitrons that way. Of course, they weren't upgraded...
I rather liked the Plasma Defender that my favorite companion Arcade made heavy use of.
MELEE: Knock-knock, pretty much, and I don't mean the Lamplighter. I wasn't a heavy melee user, though, so I gave it to Arcade too after paying a whole lotta caps to get it repaired. He pretty much killed everything with one hit after that.
UNARMED: Ballistic Fist. Wish I could've gotten it earlier.
EXPLOSIVES: No opinion. Never found enough cherry bombs to make a Bottlecap Mine