I have a rolling cart that I got at Michaels. It's officially scrapbooking storage, but it has 3 drawers plus room for magazines - vertical storage, and then a drop leaf on the top so I can open it up to about 2'by4'/ It is on wheels, so I just pull it up beside me and have my small pressing surface on that. So it's at my left side at right angles to my sewing machine.
I usually chain piece a dozen or so, and then press. I always press one seam before doing the next step.