Hey everyone, welcome to the page!
So, this build is a fairly balanced build that I've been using for a little while now. I originally wanted to do a shock build, and it eventually turned into this.
As you can see, the build centers around Deathtrap and shock damage. Its also fairly tanky, too. As a result, you can do fairly well at nearly any distance.
So, lets get into the details.
Little Big Trouble
More Pep - 0/5 - See below. You could put a point into this if you had a class mod that boosted it, but its a lesser option apart from that.
Myelin - 5/5 - Basically, More Pep is awful. It doesn't provide nearly enough benefits to make it a decent option. Myelin give you a little more shield and less of a crippling weakness to electricity.
Shock Storm - 2/5 - Shock Storm is a decent option, since it does do a fair amount of damage. However, it isn't very good unless there are a ton of enemies very, very close together. Splitting your points with the other options is usually better.
The Stare - 0/1 - Fire isn't a very good elemental type late into the game. You'll be seeing a lot of loaders and the like, and it'll usually be better to have Deathtrap shoot electricity, which you'll have buffed later, than fire.
Strength of Five Gorillas - 3/5 - Pretty much just a Deathtrap buff. More melee damage is never a bad thing to have on you, either.
Electrical Burn - 0/5 - Again, fire isn't a great damage source lategame. This one is a lot better than The Stare, though, so you could put points into it instead. Its worth noting that the fire chance is for every time you deal shock damage, including aftereffects.
Shock and AAAGGGHHH! - 0/1 - This skill can be pretty dangerous sometimes. You have to stay very far away from barrels, and the shockwave could potentially notify enemies to your presence.
Evil Enchantress - 5/5 - This is really, really good. An additional %30 elemental damage boost kicks ass, and since you'll be doing quite a bit of shock damage, this will add up quickly.
One Two Boom - 0/1 - The damage from the orb itself is great, no problems there. However, if you need Deathtrap immediately (possibly to serve as a distraction), this skill will ruin any chances of that. Deathtrap takes forever to fire this thing off, and doesn't move until you shoot it or it disappears, which wastes quite a bit of time on his timer.
Wires Don't Talk - 4/5 - Just trying to maximise the shock damage. You can only put four points into this skill if you want to put a point into Sharing is Caring. If that doesn't appeal to you, put that point here instead.
Best Friends Forever
Close Enough / Cooking up Trouble - 5/5 - Ask yourself this. How good is my aim? How accurate are my weapons? Will I need Close Enoiugh to keep up my damage? Think about it, then distribute the points accordingly.
Fancy Mathematics - (0-5)/5 - Keeps the shields up as often as you can.
Buck Up - 0/1 - Buck Up is actually broken. Occasionally, Deathtrap will head over to an enemy with a damaged shield and repair it for them, while they continue shooting at him. I'd keep away from this one until Gearbox fixes it.
The Better Half - (0-5)/5 - Fire rate increase is never a bad thing.
Potent as a Pony - 0/5 - This is an okay skill, but there are better options.
Upshot Robot - 1/1 - This is the better option. Each time Deathtrap kills something, his timer length increases. As a result, you can have Deathtrap out for a really long time. Also, damage buff for each kill.
Unstopable Force - 4/5 - Movement speed and shield regen is really nice in close quarters. You can very easily ambush someone, then dash off to the next one, while your shelds regenerate at a good rate.
Explosive Clap - 1/1 - This is pretty much the best thing ever. It does a TON of damage, easily one shotting most trash mobs, while taking a huge chink out of tougher enemies.
Made of Sterner Stuff - 4/5 - More damage resistance, more melee damage for Deathtrap. If you really don't care for this, you could easily relocate some of these points into anything else in the tree, really.
20% Cooler - 5/5 - At this point, it should be obvious that Deathtrap kicks ass. So, we keep him out as long as possible with Upshot Robot, and we get him in a soon as possible with this.
Sharing is Caring - 1/1 - This is really nice. You can give Deathtrap the same shield as you. Want him to do more damage? Equip a Maylay shield. Need him to not die so easily? Adaptive shield. There's a ton of ways to abuse the crap out of this, have fun with all the legendaries' side effects.
It should go without saying that you'll want a shock weapon for this build. Maybe two. Three? Whatever. Point is, you want to be dealing lots of shock damage, and your guns should reflect that. I suggest having one shock gun for one range, another shock gun for a different range, a corosive weapon that's good at many ranges, and a sniper rifle for picking off distant enemies.
Regarding specific guns, again, anything with shock is a good choice. A shock Infinity is a good choice, as is a shock Bitch and a shock Conference Call. You may even opt to try out the Chulainn on this set; slagging yourself is a dangerous drawback, but being able to slag your enemies will increase your shock damage (remember that the Chulainn slags and electrocutes), as well as let Deathtrap rip through the slagged enemies.
In general, you'll want something with a large capacity, possibly a Pangolin shield. The buffs from Myelin and Fancy Mathematics will make it difficult to pierce through the shield. On the other hand, if you want to take full advantage of your resistances, bulk, and Cooking up Trouble, an Anshin shield will make you very, very bulky.
Taking advantage of Sharing is Caring is a big deal, as it can greatly increase Deathtrap's effectiveness. Roid shields are nice, as although they might not be the best for you, the are incredibly useful for Deathtrap, who will rarely have his shield active. Nova shields and spike shields are great options too, as Deathtrap will constantly be in a good plave to use them.
Good specific shields include the Black Hole, which Deathtrap can use offensively while giving you easy Second Winds, the Evolution, which gives a health boost and health regeneration, and the Flame of the Firehawk, which allows for continual Fire Novas once depleted, turning Deathtrap into a floating flamethrower of chopping and exploding death.
Worthwhile class mods include the Zapper, Technophile, and Catalyst mods, while of course the Legendary Mechromancer mod is going to be your best bet.
Anyways, I hope you have fun trying out this build!