Even though the omniframe suggestion thread only allows for 2 bilities, I believe big g will give us access to at least 3. That is going to be my assumption going forward.
Now, people are talking about combining turrets with turret mode. This is not a good idea, at least when thinking about a single omniframe. The reason for this is since turret mode makes you stand still, you want ranged weapons and weapon buff abilities. So I would suggest using turret mode with heavy laser mg, penetrating rounds and resonating bolts (assuming we can use that ability with a machinegun) or adrenaline rush
Next is the ultimate support frame. This one assumes that the chosen drone is an ability and combines it with supply station and healing generator, in effect making a "med camp" on the battlefield.
And of course there's the obvious og bastion build, tesla rifle, heavy turret, multi turrets, and sentinel pod.
That's all I got so far.