LITTLE BIG TROUBLE
Bullets are fine, but elemental damage is an underrated effect that hurts enemies over time. Shock and electric attacks are key here.
Shock and 'AAAGGGGHHH'
Pandora weapons manufacturer Torgue makes guns so shoddy that reloading causes them to detonate. This power runs with that, causing electric damage when you run dry.
One Two Boom
Deathtrap fires an energy orb. Shoot it to make it explode and deal shock damage. The orb's relatively hard to pick out in a crowd, so this is a good power for marksmen and those with precision.
Make it Sparkle
Shoot Deathtrap with an elemental weapon and he'll deal damage of that elemental type. Corruption, electric, shock and slag all work.
This is arguably the most complicated tree in the whole of Borderlands 2, one for fans of damage accumulation, complex buffs and risk/reward. Know what you're doing and the pay off is massive.
For every enemy you kill or magazine you empty, you'll get a stack of anarchy. The bigger the stack, the more your damage skyrockets, but your accuracy suffers massively as a result (try combing this with Close Enough to lessen the negatives effects on accuracy).
Another new melee action for Deathtrap. Level up this alongsid Explosive Clap and Make it Sparkle and he'll be a force to be reckoned with.
The Nth Degree
On the first level this doesn't seem like much - every seventh bullet will ricochet off a nearby bad guy, Level the skill five times, however, and almost every bullet you fire will hit an additional enemy.
There's more to the DLC than Gaige herself. You'll also get the Gearbox Gold Gun Pack (a pair of two unique golden guns that you'll likely discard for better ones after the first hour), one Golden Key which unlocks rare items in a Sanctuary Loot Chest (it's next to the fast travel station and best used after level 20 or so for a higher chance of good gear), and the Vault Hunter's Relic, which grants a 5% better chance of finding rare items in the field.
Ultimately, the best advice is to find out what works for you and use your skill points accordingly. Good luck and happy vault hunting!