Probably the single most helpful tool that I didn't already have was a small bandsaw (POWERTEC BS900 9-inch). My build needed a bunch of cuts to fit things around existing molding, as well as several custom-shaped rails and brackets. I have a handheld jigsaw but the bandsaw made these sorts of cuts so
I got the usual Porter-Cable pancake compressor and upholstery stapler, which definitely sped up the stapling. Protip: go ahead and buy some ear protection while you're at it, because when you've got your head near the stapler in order to line things up by sight, that sucker can be ear-ringingly loud.
I also got an Arrow TT21 "forward action" hand stapler which worked very well for smaller staples.
I picked up a hand-held miter/anvil cutter (Lowe 815-1000) which was a bit pricey but easily chomped through some plastic pieces I needed to trim to size.
For cutting fabric I got an Olfa rotary cutter and some long metal straight edges. I got two big 2'x3' self-healing Alvin cutting mats so I could lay them down next to each other for a single long cut. By the end I was tempted to get a few more mats for even more work surface. A Clover Chaco Liner chalk pen worked really well for marking the fabric -- it draws a bright fine line of dry chalk dust and after you're done you can just brush it away with your hand. Some small embroidery scissors came in handy for trimming fraying threads.
There was also lots of little stuff, such as several additional tape measures so that when going between the ~4 different places I was working on things I'd always have one nearby.