Been through this on my old coupe last winter and picked up a few things the hard way. Before you touch the grinder, poke around with a screwdriver and map out where the rot actually ends. It always goes further than it looks. I marked my cut lines with paint pen, staying well clear of the seat mounts and the crossmember, then cut the bad metal out in one piece so I coud use it as a template for the patch. Cut a couple of inches past where the rust visibly stops. Shiny looking metal can still be paper thin, so tap it with the hammer and listen. Dull thud means it goes.
For the patch itself, I made card templates first, then transferred to sheet and trimmed untill it dropped in with a small gap. Tack it in a few spots, check it sits level with the surrounding floor, then stitch between the tacks and let it cool between runs. Jumping around the seam keeps the panel from pulling out of shape. Seams got seam sealed top and bottom afterwards, then a coat of chassis paint before the carpet went back in.
One thing, keep a fire extinguisher or bucket of water nearby when grinding and welding. Underseal and old dirt smoulder way longer than you'd expect.