It depends on how well and how quickly you currently can cut fabric by hand. If you are pretty accurate, I would bypass the strip cutters and go for a quilt that is difficult to cut by had, such as winding ways or drunkard's path. If you do a lot of appliqué, then cutting shapes, such as flowers etc. may be a good choice.
you need to see what dies they have available before your session. They may have a list. When you have made your decision, precut your fabric into appropriate size pieces at home. Folks on this board can help with the sizes. If you are going to cut appliques consider ironing on fusible before you cut. One hour isn't a long time, so preparation will maximize your time!