I cut off the aesthetically pleasing side of the selvedge with about an inch of the fabric pattern as well, depending on the type of fabric.
For your selvedge fabric project to turn out best, I suggest taking a few minutes to come up with the order and placement of your selvedge strips.
Start with the selvedge edge (cut to your preference) and lay it down on your backing.
When you place the second selvedge strip down, do so in a straight line, making sure it entirely covers the cut fabric edge of the previous strip to curb fraying.