I would say 6 is a decent mayhem to try as with enough rolls its not bad and it gets you all the gear
It is possible to get by without DLC guns, you just have a ton more options with DLC guns. For Gamma Burst, the stronger damage setup is using guns with the 50/150 Rad annointment. The Reflux with that annointment is one of the best guns non DLC guns. Some other good guns are:
Hellshock, Maggie, The Monarch, Backburner, Plaguebearer, Kaoson, Sandhawk, Hellwalker, The Lob, Brainstormer
There are definitely more guns that can be used, especially with some of the more recent gun buffs. Just have not had a chance to try them yet. Note though that the annointment will make a huge difference even on underperforming guns.