Lots of good info here. I just got the Accuquilt Go BIG (the electric one) and bought the strip bundle--which not only cuts strips of sizes 6.5, 4.5,3.5,2.5,1.5 &1"--these can all be subcut into squares or diamonds, or rectangles. I also bought the triangles in a square (like the Tri Recs rulers cut). It is so precise, quick and doesn't make my "bum" shoulder hurt.
I also have the Shilouette Cameo--it attaches to your computer and you can either download designs, use the program to draw your own designs, or scan a design in. It cuts paper, cardstock, vinyl, and fabric that has a fusible on it--only 1 layer at time. The Cameo is great for applique, but not practical for pieced work. I bought it so I could use it for all the materials listed and hoped it would encourage me to do more applique. Haven't really used it much for applique, more for other mediums. Will say it cuts fabric better if the design is not too complex.