This build is a typical Phasezerker set-up, utilizing Ties That Bind to spread DOTS and explosions all across the battlefield. You can really use any weapons you want, but I would recommend Lightshow's, Monarch's, Refulx's, or anything that is good in your opinion. The shield is also your choice, but I would also recommend the Old-God shield or the Plus-Ultra, but if you don't have DLC, the Transformer is fine. For the grenade, it can literally be anything, but I would recommend the Hunter Seeker for that Pearl stacking. The class mod will obviously by the Phasezerker, and the relic will be the Pearl of Ineffable Knowledge, but, again, if you don't have DLC, than a Snowdrift will do fine.
Guns: Consecutive hits or 100 ASE. Shield and Grenade: ASE 50% Elemental Damage.