Edited for december patch
Now that we have burn cards its easier to get your hands on a phoenix/bareth which is good because you don't have to run weapon scavenger or pray RNG to get one.
You still have to find a decent sidearm though, so weapon scav is still really good early on, but once again you have the burn cards for that too.
Note that you could play any weapon in this deck, there's nothing restricting you from playing a sniper. And you can loot anything until you find a phoenix. I also played a variation of this deck with "two is one and one is none" and "weapon scavenger", so every decent weapon I found I could equip.