I have a 36 inch ruler, looks just like a yard stick, maybe a tad bit wider. I found it at Joanne's with the other quilting ruler. I don't use it all of the time, but it does come in handy.
I also have one of the cutting mats you are talking about. I'm lucky, it's the exact size of my kitchen island, so I use it there to cut fabric. I use some of the spongy shelf lining stuff, a six inch strip on both ends,between the mat and the counter top to keep it in place. Works really good!!