I don't have very many mutators atm, but I'd say either bandit or the one that increases ranged damage as you pickup ammo
For my long gun Im using the bonesaw with overflow and bandit mut. And I've been switching the sidearm around depending on the situation but I've found that enigma works well in many many situations with many different mutators. I'm still not done with my first run through though, so I'm still on the lookout for a new favorite lol
That'll probably be the way to do it for a while. Tragic just made a post on Reddit about making tweaks and changes to stuff, like scrap and material rewards, so we'll see what happens
The best thing I've found so far is just to run adventures. Once you get a few levels into the archs and start getting a build going you don't need to upgrade as much allowing you to start saving more. I was able to come out of one up 5000 from when I went in. Ofc results may vary depending on where you are and it may take a surprising amount of time if your build is lacking. I personally have not found any trinkets that increase the amount of scrap you collect but there were a few of those in R1 so it might be worth it to look out for those as well. Another thing: don't worry about collecting things you already own. Often times when you pick up a ring or something which you already have, it gets converted into scrap.
Started challenger and picked up medic pretty early. Got a ton of trinkets that lean towards shield so that's what I've been running for a while. Got both up to 10 and really had fun with them. Been trying to switch up archs to get levels spread around and to give more archs a shot but I've had a rough time of it sense low level archs don't have much going for them