> most people advise against a square or rectangle room <
Yes, but with a space as small as yours I don't think you have much choice. Anything you do to make the shape different will reduce the work space and room size even further.
> I've recently read a lot of anti-carpet stuff, mostly on this message board. <
Yes, much better to leave the floor reflective, or maybe have a small area with carpet, and treat the ceiling to be totally dead to as low a frequency as possible.
> I'm planning on mounting 5/8" sheetrock to resilient channel on the ceiling, as I will need some degree of soundproofing from above. <
Even with a layer of sheetrock you'll still get some sound upstairs. It may not be worth making the ceiling lower for the small reduction in sound transmission you'll get. Note I said may as I can't say for sure how much difference one layer of drywall will make. One huge advantage of leaving the joists exposed is you can then apply a substantial amount of ceiling treatment between the joists, without making the ceiling any lower at all. Then you can cover it with fabric.
> What type of traps/how many would you recommend for a room this shape and size? <
As many as you can fit. Seriously. A small room needs more treatment than a larger room, and eight traps just for the corners is the minimum you'll want. A few more on the walls will be even better.