Is there a preffered, or standard, way of building a soffit, such as that for kitchen cabinets? I've got a few questions.

Should I install the drywall first then build the soffit and drywall it, or should I frame it and drywall all at once?

Any reason why I can not use 2x2s or 2x3s for the soffit? With a 2x4 costing 2.65 these days, it'd be some savings.

I've got a beam that I'll need to frame around and then drywall. It's perpendicular to the cabinet soffit. Let's say the cabinet soffit is 12in deep and the beam is only 8in deep. Should I frame the bare minimum around the beam (8in) or match it up with the cabinet soffit all the way across the room? I really don't want to lose the head room, or divide the kitchen. Ceilings are 8ft 6in.