So, people is so hot in Marion Tavares decks with Fortune trait and The Book of War builds, people forgets she is a Guardian and she can run weapons.
If you can only run a one hand gun, just run the best gun there is.
Marion is all about action compression. Marion can play those events that synergize well with guns at instant speed.
Play gun, shoot for free. Play Hunter's Mark and then play by the face thanks to Marion ability Hand-Eye Coordination to shoot for free again. Those can easily be 5 damage for 5 resources and 1 action, which isn't bad at all. You are testing at 5-6 base, but this can be worked around with allies like Beat Cop or Grete Wagner at level 0, and then be improved with Good Weather, Reliable and a long sort of events, upgrades and assets.
You can tutor for the gun with Prepared for the Worst from your Stick to the Plan pile and then play any other event like Emergency Cache or Stand Together to generate tons of value prior to pay for any future shenanigans, like the gun itself.
Support your gunning with some fight events to keep pumping the damage, and when you play your second gun after using your ammo, discarding automatically your first one due to your unic hand slot, shoot again for free! Maybe you don't have your second gun at hand, but then you can just use Act of Desperation for a potentially 4 damage 1 action and use Marion reaction to play a money event or just a tutor, preparing yourself for the second gun.
The level 4 gun is an adequate upgrade. It will get Marion to a base 6 to combat, but this should do the trick while you flesh out the most urgent things in the build. Just please, don't rely on your events in the early scenarios since you won't have tutors for The Book of War and One-Two Punch, Just reinforce your chances at fightning using the Remington Model 1858. No other Guardian will abuse the hell out of this better than Marion.