After I have stabilized the quilt with stitching horizontal and vertical, do any of you stitch around the outside edge before putting on the binding? Thanks for all your help--I learn so much from this forum!

I do stitch around the edge before I put the binding on.

me too :D

For me, it depends on the density of the quilting pattern and whether it goes all the way to the edge. I do not usually stitch the perimeter before sewing on the binding because the quilting is enough to stabilize the edges.

No I dont
But it is important to square up your quilt before binding.
If you machine stitch in the ditch it keeps your seams from being all wonky.
I use a walking foot to attach the binding to the front then I use a stitch in the ditch foot to attach the back binding. Love that foot as it keeps my seams right in the ditch.
I learned from this board to use Elmers glue to hold the back binding in place before sewing, much better than pins. Thin line of glue then iron.

Same here. Do not cut the batting and the backing down until you have either stabilized or put on the binding ...

I used to not cut off the backing and batting before putting on the binding but have found it is more important to square up the quilt before binding.
I machine stitch my binding in the ditch rather than hand stitching and squaring up the quilt is very important.

I should have taken a bit more time ... I used to cut the backing and binding right down to edge of the quilt. I don't have the space to lay the quilt out to square it up, and for some reason, that hasn't been an issue. However, cutting things down while walking around the edge of a bed (and, yes, I did cut a sheet doing that little trick, too! <g>) anyway, I found that if I cut too close to the top, I would inevitably run out of batting and backing somewhere along the way. Now, I trim the batting and backing to with two inches or so from the top ... if you leave too much backing and batting, it is a constant battle to keep the edges smooth.

That's what I do, too!

stabilizing the edges before putting on the binding would probably eliminate a lot of fiddling to ensure capturing all of the front and back and ease any "waves" as you go along. Trying to do all of that at once sometimes becomes a bit overwhelming.