Get the suction cups at Harbor Freight for about $6. They are the same except for the color as those sold at quilt shops for about$30. I have both and use them all the time. I use to have problems cutting long pieces, but not anymore.
Also if you want narrow strips, you may want to get the Simplicity rotary cutter. It works O. K. if you will take the time to adjust it for each type of fabric. Then you have to feed it straight, but it's really fast once it get it figured out.