Ultimate build? Probably to peoples' tastes, but all of the Striker builds will be similar.
Here is the build I would use as a baseline.
I say baseline, because I don't know what weapons you'll be carrying or what augs you'll have put on them, so just get things to that area. Note that I'm assuming you'll have a +1 Engineer Skills helm.
Note2: Hastebot 3 is all you'll need since you'll find two single hand weapons with Hastebot 3 on them, plus the helm, keep them on swap so that you switch to them whenever you enter an area and you'll make a 10/10 Hastebot.
Because the Engineer doesn't get Multishot, their Strikes are more powerful than the MM's; they get weapon elemental strength effects, criticals, the synergies seem more powerful, and best of all, the +splash area mods in your weapons will effect the strike AoE.
IMHO, the best skill in the game is Smackdown. It does a lot of damage and it has a HUGE stun strength (that will stun even bosses like Moloch for a time, but more importantly, his summons will be locked up). When you are power leveling, if you do that sort of thing, you'll be the most valuable member of the team that is doing the "First room SH only, speed runs!" PUGs. You'll zone, throw in the Smackdown, and everyones' exp bars will start visibly moving up, rinse-n-repeat. Napalm is good too, don't get me wrong, it just doesn't have the crowd control aspect that Smackdown has, and really, when you are in a room filled with dangerous foes, stunning them all is the best damn thing since sliced bread...as a matter of fact, I think they have officially declared that Sliced Bread has lost its crown of excellence to Smackdown. Shock and Awe is *useless*, never use it, just get it for the AoE synergy.
Drone --> typical little tanker. Like with HGL, give it the Hell mode Wirt's Leg, so that it is forced to go melee range with the boss/foe, and then sit back and do your thing. If you got spare points, put them into Master Engy. Up until you get to the higher levels, you might consider giving your drone Moyer's, since that seems like a good match for it (low feed requirements).
Bots --> Hastebot, as mentioned above, to 3. Rocket bot, it's a nice opening salvo, plus with Hastebot, you pretty much can spam spawning the Rb and then Molotov at will, which is not too bad, although in a long fight I usually prefer to let it spit rockets at the target occasionally instead of feeding the boss a steady diet of the Molotov inferno...but, that's just me. Spiderbot is the new toy, and it is pretty effective/fun.
Quick Buttons you should use, in order of importance;
1. Smackdown
2. Napalm
3. Molotov
4. Rocketbot
5. Repair Drone
6. Construct Drone
7. Spiderbot
8. Beacon
9. Escape
0. Tactical Stance
With a modern mouse (thumb buttons & wheel button), you should be fine.
Open with Smackdown. Throw on a Beacon, do a TS, start firing on targets. If anything is left alive, throw out Napalm, and follow up with a Molotov Assault or Spiderbot depending on your preference. Escape is your OS skill, but you won't need it often. Alternatively, you could drop a point in Phase Grenade, let your Drone gather the mobs, toss the grenade and then follow up with a Molotov or Napalm...it's all effective.