The Adept is my favorite character class in Mass Effect 2. These are the play strategies that I use for the Adept.
The first type of adept that I play with is a strategic adept. The bonus weapon that I use for this type of adept is the Sniper Rifle. I equip the Viper because there is no time slow down bonus for this class. For class powers to be used, I mostly pick Heavy Singularity, Unstable Warp, Heavy Throw, Pull Field, and Bastion. The sniper rifle is for distance and power enemies such as Ymir Mech or Harbinger. The class has the submachine gun for close quarters fighting and the pistol with all biotic powers. The armor upgrades that I pick range from either health heavy to biotic heavy power options. This is a lot of duck and cover play and I have found that the most difficult times I have with the build is when Husks try to come close in.
The other type of adept that I play with is a run and gun type. The bonus weapon you choose is between the shotgun and the assault rifle. I choose the assault rifle but both work fine. I have done both. The bonus power I choose is Heavy Barrier. All armor options are for weapon and shield related perks. I choose the Nemesis line for even heavier damage done. Heavy Singularity is used as well as Heavy Warp and Heavy Throw. I find this to be a superior build then the strategic type. I am able to take on any combat situation with this class build.
For both classes I have squad mates that have either Heavy or Area Overload. I always try to make sure that whatever squad mate I am choosing to come with for the mission has a squad ammo power for both class builds. I tend to use Thane, Jack, Garrus, Grunt, Kasumi, Mordin and Miranda a lot as squad mates. For Thane, Jack, Garrus, and Grunt I make sure their ammo power is a squad ammo power and I select the rest of their powers to suit how I play. I make sure that Miranda and Kasumi have Overload maxed out, and for the rest of the power selection that is up to you. I would say that this is how I use their powers but I am constantly changing them once I go take on the Shadow Broker. Other then what I have mentioned as static for powers, I change them a lot. This is how I play ME2 with the Adept.