I always cut the excess off once I've quilted my sandwich. It's not a good idea to use binding that is cut with the grain of fabric....... straight with the selvage or cut edge. The reason I was told is because with the straight of the fabric there is only one thread that runs along the edge and it will get worn and tear with use. I know that is true because I have several old quilts that have the binding worn along the fold. If you use bias strips you will have 100's of threads along the fold and they will make the edge stronger and less chance of wear.
I cut my bias 2 1/4" and fold it in half. Then, I sew it onto the quilt using a 1/4" seam. 2 1/2" width binding works well, too, like bigsister63 said. You'll want to check out some of the tuts to help you do the corners or round off the corners and you won't have to worry with that. Then, I turn the folded edge to the back and hand stitch it in place.
Good luck..... let us see your finished project..... I'm excited for you.
nanna