For myself: This Machine & Love & Hate.

For companions: Pushy, Oh Baby, All American & Gobi.

I took This Machine it is very versatile.

pew pew is a close second, because of the whole pew pew thing.

Maria, I felt like a somebody with that gun on me.

For Power: YCS/186
For Entertainment: Mercy
For Looks: Tesla Beaton-Prototype
For Easiest to Use: Maria (Yes, the unique version of one of the first weapons is easiest to use)

Depending on play style. :

Oh! Baby
Q-35 or Holorifle
Ratslayer
Pushy

If I had to pick just 1 though, it'd be Ratslayer. I think it was my first unique. Found it en route to cottonwood cove, and it lasted me throughout the entire game. I was headshotting chumps in the Legates camp with that thing.

The only way it could be any better, is if there were hand loader 5.56 rounds to send downrange.

That Gun, for reasons I've stated before but will state again. It's from the movie "Blade Runner", and without it my character (a reprogrammed replicant in a Mojave to track down others of his kind) would seem a bit out of place. If only I knew how to mod I could really get crazy. *Sigh*, oh well.

Surprisingly, it's not This Machine. Forgive me, Woody.
My favorite unique firearm is Thump-Thump.
OP didn't list any unique melee or unarmed. :sadvaultboy:

I love 'Dinner Bell' but cant see it on ure poll, so put down That Gun (after patch)

"That Gun" and Avenger for my Guns guy...
But since I'm mainly a EW guy, I love Tesla-Beaton =) (Especialy the Tesla part)
And Pew Pew is great for minor targets, same goes for Pulse gun (Even if it's just aginst bots)

I don't think I ended up using any of them except for This Machine..
As far as looks go I thought Maria had the best customized design.