The 'machine' I would recommend first would be two good folding saw horses, a 3/4 inch piece of ply wood and a helper. Or a new back right after you are done. Take your pick.
I'm a beginner with upholstery, but I now have a few tools to help. Step Son Stair Tool, vapor steam cleaner, VS upholstery unit. I've just started using the vs system. All three ways seem 'best' given any number of situations to get about the same results. The steamer is nice for really trashed stuff, but also more risky to use because of potential for heat damage. The stair tool is good on UP that doesn't have much contour (buttons, folds, etc.), but not so good on big fluffy and loosely stretched fabrics. It's also heavy. The vs machine seems the best all around unit so far. I also keep a couple hand brushes nearby. One has soft bristles and one has medium bristles. Helps with the hard to get at places.