Best......

Pistol
Rifle
SMG
Shotgun
Heavy Weapon
Energy Pistol
Energy Rifle
Energy heavy weapon
Explosive
Melee
Unarmed

You don't need to have an answer for every category, just try think of some

well,for unarmed i think ballistic fist and for rifle is this machine(kill commies)

Rifles: Anti-Material Rifle, without doubt

Pistols: Mysterious Magnum

Shotguns: Don't really know. I've only used the Lever-Action Shotgun

Energy Rifles: YCS/186

Meele Weapons: Oh, Baby!

Unarmed: Ballistic Fists

Explosives: Bottlecap Mine

These are just my opinions.

Pistol: Mysterious Magnum
Rifle: This Machine
SMG: 12.7 mm Submachinegun
Shotgun: Riot Shotgun
Heavy Weapon: Automatic Rifle
Energy Pistol: Plasma Defender
Energy Rifle: AER14
Energy heavy weapon: Plasma Caster
Explosive: Mercy
Melee: Shishkebab
Unarmed: Ballistic Fist

just my opinions

These are ones I happen to like:

Pistol - Maria. The weathered 10mm is a bit more destructive, but you can't hide it in a casino no matter how high your Sneak is. I don't like pistols much, except as hideout weapons. For combat, rifles are just better.
SMG - 12.7mm SMG with silencer. The spread is a pain, but it's an awesomely deadly weapon.
Shotgun - No opinion, I don't use them much.
Rifle - Assault Carbine with AP ammo. I realize there are better guns out there, but this one is a simple, efficiant Legionaire-killer. And ammo is unbelievably plentiful.
Heavy Weapon - CZ-57 Avenger. Just discovered it, and I LOVE it. Want to do a character with 7 STR and WH perk, plus 100 guns, just to make ideal use of it.
Energy Pistol - Don't really use these myself, but I love Arcade's Plasma Defender.
Energy Rifle - Q-35 Modulator. Reminds me of my beloved A3-21 from F3.
Energy heavy weapon - Incinerator. Great for heavily armored foes, as well as impromptu cremations. It never quite feels right leaving dead bodies lying around to rot - they let you exhume graves (which I never do), but they don't let you bury people. I'd think that would be a karma-building act.
Explosive - Grenade launcher. Nice for closely bunched batches of fiends.
Melee - Shishkebab. Sword good. Fire good. Fire + Sword better.
Unarmed - Ballistic fist. Me with one + Veronica with one = Epic Annihilation.

Pistol - I let Raul use the 12.7 Pistol and he seems to be capable with it.
Rifle - I like the Trail Carbine, I think Brush Rifle is better but it's ammo is hard to get for me.
SMG - Laser RCW+, it's a beast, took down entire Deathclaw Promotory with it.
Shotgun - :shrug:
Heavy Weapon - Missile Launcher for sure, that thing is a beast.
Energy Pistol - Pulse Pistol, straight up.
Energy Rifle - Holorifle+++, YCS is better in DAM with each shot but it takes such a long time to reload and wastes A LOT of ammo.
Energy heavy weapon - Incinerator, not for endgame but for early to mid-game it's a beast.
Explosive - I love the GMG, Incendiary Grenades and C4, can't choose between them.
Melee - :shrug:
Unarmed - Pushy!

Pistol - Always liked taking out the 10mm pistol once in a while. I don't use pistols all that often.
Rifle - I'm inclined to say the All-American for it's well balanced abilities and use of common ammo.
SMG - No clue if its Guns. If I'm allowed to use the Laser RCW, then that would be my pick.
Shotgun - Hunting Shotgun / Dinner Bell. Took down a mod with it alone.
Heavy Weapon - Not enough experience with them.
EW Pistol - Pulse Gun.
EW Rifle - Holorifle - seems unfair to use it so I just stick with my AER14.
EW Heavy Weapon - Don't use them all that much.
Explosive - Grenade Machinegun and / or Annabelle
Melee - Shishkekab
Unarmed - Ballistic Fist

-Gunny out

Pistol - 10mm Pistol with all mods and loaded with JHP ammo
Rifle - Trail Carbine, scope mod and SWC ammo.
SMG - 10mm SMG with both mods and loaded with JHP ammo.
Shotgun - Leaver-Action Shotgun, magnum buckshot and key perks.
Heavy Weapon - Auto rifle loaded with JSP ammo. 440 DPS love.
Energy Pistol - Humble Laser Pistol
Energy Rifle - Holorifle.....by allot.
Energy heavy weapon - No idea
Explosive - C4
Melee - Chances Knife
Unarmed - Ballistic Fist scares me the most. So I'll go with that.

Pistol: 10mm Pistol
Rifle: This Machine
Sniper: Anti-Material Rifle
SMG: 10mm SMG
Shotgun: Hunting Shotgun
Heavy Weapon: Automatic rifle
Energy Pistol: Pew Pew
Energy Rifle: YCS/186
Energy heavy weapon: Euclid's C-Finder
Explosive: Grenade Machine Gun
Melee: Chainsaw
Unarmed: Ballistic Fist

Pistol Mysterious Magnum
Rifle Trail Carbine
SMG RCW
Shotgun Hunting Shotgun
Heavy LMG (I don't have Dead Money or I would say the BAR); or classify the AMR as heavy - is anti materiel
E-Pistol Plasma Pistol
E-Rifle Laser Rifle
E-Heavy none...or just classify the YCS as heavy
Melee chances knife
Unarmed power fist

notice "best" does not mean "most powerful on paper",
I took "best" as most useful.

The best weapon is the weapon you can hit the target with...and find ammo for.
Doesn't hurt if you don't have to fix the friggin thing every five minutes either.

Pistol:Ranger Sequoia
Rifle: Trail Carbine
SMG: Laser RCW
Shotgun: Multiplas
Heavy Weapon: Automatic Rifle
Energy Pistol: Plasma Defender
Energy Rifle: Holorifle
Energy heavy weapon: Heavy Incinerator
Explosive: Annabell
Melee: Oh!Baby
Unarmed: Ballistic Fist

Pistol - Weathered 10mm Pistol
Rifle - The Gobi was better before it was reduced in the last patch. I modded it back up and love it.
SMG - 12.7 mm Submachinegun
Shotgun - I don't use them but Cass loves the Riot Shotgun.
Energy Pistol - I had a great time with the Recharger Pistol - loved that it didn't use up ammo.
Energy Rifle - Never shot an EW that I didn't like. I'll say the Q-35 Modulator or the Tri-Beam.

Energy heavy weapon - Incinerator is great; great to arc the trajectory and fire at the Deathclaws.

Explosives:
Projectile: Thump Thump and the Missile Launcher
Thrown: Pulse Grenade, Look out ED-E. Fire in the hole!
Placed: C4

Melee:
Bladed: The Broad Machete is the one I've used most...have to try the others yet.
Blunt: I haven't used these yet.
Thrown: I've only used the spears and they were fun early on.

Unarmed - Love and Hate. I just made my first-ever build for an unarmed character. She's Unarmed/Melee/Explosives and she's using Love and Hate and she's handling everything Boone doesn't get first. I'm very surprised since I've never done this build before and it's a lot of fun.

Pistol- Silenced .22 pistol
Rifle- Varmint Rifle
SMG- 9mm SMG
Shotgun- Single Shotgun
Heavy Weapon- fat man
Energy Pistol- laser pistol
Energy Rifle- laser rcw
Energy heavy weapon- gatling laser
Explosive- dynamite-
Melee- straight razor
Unarmed- my boot