Mine would be the Lincoln's Repeater. Has an overall good damage output, can easily be repaired with hunting rifles and cost less AP in VATS.

The A3-21's Plasma Rifle was mine.

Deathclaw Gauntlet from the Bear Brothers. You could essentially kill everything with 100 unarmed with that.

You are right on the Lincolns Repeater its the most economical weapon in the game in my opinion. I'm also a big history nerd and the whole idea behind it is what makes it a main stay in my inventory. I never wander without it.