Do the strike quests for the weapons too. There is a good heavy machine gun edgewise, the loaded question is good....Gambit has awesome weapons too like the 21% delirium, breakneck, clean getaway. Those are all good weapons to grind for.
Go see Ada (way left in tower) and open up the forges. They have some good weapons to grind too. Pulse is good, the HMG from there is good, they also have a bow, AR, hand cannon, and snipes you can keep grinding to get good rolls. I recommend the HMG and pulse first.
All these will set you up with some awesome weapons to start. and yeah look for outlaw (quick reload) and kill clip, rampage, swashbuckler, are all DMG buffs for weapons that make them do more dmg. Look for others that give you +range, like high caliber, ricochet rounds, feeding frenzy also buffs reload, there are others like grenadier which are good because it gives you nade energy when you kill with it.
Download DIM and log into it with your steam. This will give you some hidden stats on weapons that you dont normally see. Plus it allows you to swap weaons to/from vault or character to character. It also lets you transfer weapons from postmaster to your character without going to tower.