I started right out on real quilts too. Worked out fine! (I did have some experience FMQing on my domestic machine.) If you feel the need for practice, instead of muslin you might want to try used sheets from the thrift store for top and backing. Afterwards you can cut up and bind for pet shelters (call the shelter first to get info about sizes and fabric/batting content).
As for cutting the backing straight, you may be over-stressing about it. How it is cut isn't really the issue; how it is mounted on your frame is what's important. I would recommend investing in Red Snappers if you can add casings to your leaders; makes loading much easier and faster. There are lots of Youtube videos on the Red Snappers, but in my opinion the following video is the one that both shows and explains how to load a quilt so that everything is straight on the rollers:
http://manquilter.com/
If the sound isn't good enough on this video, check out this one:
https://www.youtube.com/watch?v=yx5m...B_d7zHVyA8J7JQ
It's much shorter (I think the one on manquilter's website is better), but the sound works better on my computer.
Basically, manquilter is showing how you do not need to use measurements (or even straight cutting lines) to load a quilt evenly on rollers.