Take the Varmint Rifle off that list, that thing hits nasty hard on criticals.

No. I wont, because a crit with any gun makes it useful.

the Euclids C-Finder, powerful if you do its quest, but, it bugs ALOT and tends never to work for me :/

Well, your not the first to say that, so i will add it to the list.

Varmint Rifles do 5x more damage on criticals. A varmint rifle does 20 damage so 5(20) = 100 damage. With better criticals that's 150 damage. With a silencer, night scope, and hollow-points, it's as good as a sniper rifle, and it's a lot more economical.

Edit: with all of that a sneak attack critical does around 220 damage. That's almost as much damage as an AMR critical.

Boxing Tape.
It puts a layer of tape on your fists.

The best is Pushy of course.

Hey, who said tape was useless? It fixed an alien spaceship.

I'm refrencing the worst movie ever made, of course.

I don't use VATS and I can snipe from far enough away that I'm out of the A.I. detection range,
so they walk around looking for something or someone to attack, but I'm out of range,
so I pick them off at leisure, and get sneak attack criticals along with it.

i believe you are confused. The UNIQUE varmint rifle (Ratslayer) has a x5 crit multiplier, the standard varmint does not. Also, the crit multiplier does not multiply the damage done, as shown in your calculation. The crit mulitplier multiplies the CHANCE to make a critical hit. So if you had 5% crit chance, and you used the rat slayer it would boost your crit chance to 25%. The additional damage from a critical hit still remains at 23. In reality, with a critical hit and better crits perk, the ratslayer will do 57.5 dmg.

My worst:

Gun - BB Gun

EW - Recharger Rifle *Seriously, it has less DPS than the pistol and the same damage.* The laser pistol is alright to have but isn't something you can count on beyond level 10 at most.

Explosive - I picked Powder Charge but Time Bomb and basically any mine aside from Pulse Mine is kinda pointless. Pulse mine being the exception because you can stealth mine the battle in a certain vault, as shown in one of my videos http://www.youtube.com/watch?v=Y0wG_7n-8uw. Skip to about 10 minutes. A rare occurrence, yes, but doesn't make them useless in any case. The Crashed Vertibird is also another scenario where this can reign. Dynamite.. pretty much VATS only use.

Unarmed - Other but I actually want to say none... have you guys ever tried rounding up a pack of geckos at the start of the game and just loop around them while punching them with Boxing Tape / Gloves? Then when a few are down, resort to your fists to save condition on the Tape / Gloves, and rinse and repeat until they are dead. Saves your ammo and, if you're really good at it, you won't get any hits on you so no healing as well. Beyond that, not much use, yes, but the same can be said about Brass Knuckles as you end up getting a Power Fist / Spiked Knuckles / Bladed Gauntlet soon afterwards.

Edit: Melee - Picked Knife for the heck of it but I do believe the Rolling Pin is more useless... ah well. Lots of melee weapons I've never used.

You can't just assume everyone is going to find ratslayer right off the bat, and it's the only standard weapon with a scope and silencer on it until you get a sniper rifle.
Varmint with night scope and silencer is a great weapon for mid-low level enemies.

Eh the BB gun and the 9mm pistol are the most godly waepons Fallout series has ever embraced....

Gun: definitely .22 SMG; you can't even hide that thing from security check....

EW: Recharger Rifle. Seriously, why isn't there one in Chat's store when the Courier need one?

Explosive: Dynamite. It is just useless because it is the worst one....but in general explosives are OK.

Melee:Pool Cue. At least Rolling Pin have a reasonable reach.

Unarmed: All of them have their use, so none.

Then how the hell am I melting deathclaws with a normal varmint rifle?

Sniping is hard. What he says is correct.

I've only used EW in this game, so can only comment on them. I have found both the recharger rifle and laser pistol to be very useful at the start of the game. A well-repaired laser pistol, in particular, is very effective against Powder Gangers and the like, and of course the Recharger is great when caps are tight. I choose the plasma pistol as the worst weapon: I didn't like it in FO3, don't care for it here. Slow to fire, slow projectile, waste of space.

"All of them" is a very appropriate option for the Explosives category. Even with 100 Explosives skill and and all three levels of Demolition Expert they are distinctly underwhelming in my experience. Not to mention I managed to make all of 2 bottlecap mines in the whole game. They could pretty much drop explosives from this game altogether for all the use they are.