Saddle Stitch or Perfect Binding?
It’s entirely up to you. But here are the considerations.
Saddle stitch is harder to print, easier to bind. Perfect binding is easier to print, harder to bind. For perfect binding, your regular printer that can print up to 8.5″x11″ paper will do the trick. You’ll just adjust the guides in the paper tray to fit the smaller 6.125″x9.25″ paper. But then you’ll need to take that paper to a shop that will apply a perfect binding (tape binding will probably work here too), which involves heat and glue.
For saddle stitch, you will need a large-format printer. The reason: no matter which way you turn it, 12.25″x9.25″ is just barely too big for a regular printer. (Usually, the dimension that fails is the 9.25″, as your 12.25″ side will fit in most printers that can print 8.5″x14″ [legal] paper. But the width cannot exceed 8.66″.) But, once you’ve got it printed, all that you need is a stapler with a long arm, and your petition is bound!