I'll preface this by saying I'm not a huge fan of the Brawn tree - I have much more fun trying to pump up my DPS than trying to regenerate a health bar that goes down in 2 hits. I focused on mostly Gunlust until level 47, putting points into Divergent Likeness, Money Shot, Down Not Out, and No Kill Like Overkill. A class mod boosting Divergent Likeness or Money Shot is extremely helpful, and No Kill Like Overkill is ****ing absurd if you know how to use it, i.e. get a kill with a high-damage weapon like a shotgun, rocket, or Tediore reload, then swap to a fast-firing SMG or pistol and mow everything down.
An alternative (if you manage to find a class mod boosting "5 Shots or 6") is to fill out Inconceivable, Filled to the Brim, and 5 Shots or 6 and then put your remaining points in weapon swap skills like Quickdraw, All I Need Is One, and Auto-Loader. Wield a rocket launcher, preferably Vladof for reduced ammo per shot, and just spam rockets until everything is dead. You will literally never run out of rockets if you manage Inconceivable/5 Shots or 6 correctly. Any time you need to reload, swap to a different weapon, get a kill to activate Auto-Load, then swap back. You should not be Gunzerking very often with this build.
Once I got to lvl 47, I used either the pure Gunlust build above with the remaining points in Inconceivable/5 Shots or 6, or (my favorite) a Rampage build with special emphasis on Inconceivable, 5 Shots or 6, Keep Firing, Last Longer, and Get Some (plus Gunlust up to Down Not Out). This build allows you to Gunzerk nonstop with virtually no cooldown. The reason you have to wait until late-game to do this is because Down Not Out is super helpful for perma-zerking, and you can't access Down Not Out and Keep Firing simultaneously until lvl 47.
As a side note, a Gunzerker with Inconceivable/5 Shots or 6 maxed plus an appropriate class mod can potentially fire a Jakobs shotgun like 50 times without having to reload. The damage is absurd even without any legendary items...