In a contest between Adept and Engineer, I usually go Engineer. Just because cool gadgets and high tech weapons are, to me, cooler than space magic.
I usually build my engineer like this:
10 pts Area Overload (anti shield, anti synthetic)
10 pts Incineration blast (anti armor)
10 pts Explosive Drone
10 pts Demolisher (prefer the power damage boost to the power duration boost)
1 pt Cryo Blast
10 pts in your bonus power. Most any bonus power will work here, just pick what you like. If you don't care about a tech power class having a biotic bonus power, Heavy Warp Ammo or Reave are outstanding anti barrier powers. Reave gives you anti barrier power, health boost, and crowd control (not that you need it that much, since your drone is excellent crowd control as well). Heavy Warp Ammo isn't as powerful as Reave, but it's more versatile; it doesn't eat up your valuable cooldowns and also provides additional weapon damage outside of just anti barrier damage.
Personally, however, I prefer to use AP Ammo for my bonus slot. Makes more sense for a tech power class, and does a good job of redressing the Engineer's crappy starting weapons.
On the Collector Ship, any of the weapons trainings are good choices, but will effect how you play a lot, so keep that in mind. Shotgun works surprisingly well. Engineers are squishy and die easily, so they don't seem to be good for close quarters combat. However, the distraction the drone provides can give you room to close the distance and use your shotgun. Also, shotguns are powerful weapons against shields and barriers. Since shotguns can overcome barriers very quickly, this alleviates the need to take an anti-barrier bonus power. Shotgun Training + squad powers will be plenty for barrier removal.
Assault Rifle training is never a wrong choice, as the Mattock is a fine rifle for most situations. The Mattock isn't a god-tier killing machine in the hands of an Engineer like it is with a Soldier, however. The Mattock is still impressively powerful, but you can't use Adrenaline Rush to stretch it's ammo out. Running out of ammo with the Mattock as an Engineer is a fact of life, so don't forget about that SMG on your hip.
Sniper Training is an unusual, but interesting choice. The sniper rifle's scope can be used to target your powers on enemies at distances you normally couldn't. Even when enemies are far enough out that you still can't target them for powers, that's where the rifle itself shines. Sniper Engineers don't have the problem of being pummeled by heavy weapons in sniper positions without a good weapon to suppress said heavy weapons. In this case, the SMG is still used very frequently for CQC in conjunction with your powers.