As someone said, you most likely will be required to take a class on using the LA before being allowed to rent it - so make sure you consider that expense & time as well. Also, some LA machines are very sensitive to different types of thread, so you may not be allowed to use the water soluble. Also, loading your quilt on the frame takes a good bit of time and you may discover that you can only get one done in a 4 hour visit, depending on how big the quilt is.
Since you most likely will have to take a class before using the machine, buy the backing then so you can wash it. If you've washed all the other fabrics, I'd wash the backing if at all possible.