I am in the process of doing four Quilts by a "Quilt as you Go" method.
I pin the binding really good to the back side of my Square or Strip. I then stitch from the front side 1/4" all the way along. I then flip it over and sew the same 1/4" from the back side on top of the binding piece. It takes more time but, if you missed anything on the front, you catch it on the back.......It can never come a loose period.
I also do this same 1/4" sewing around each block or strip that I am working on. It just gives your work more stability.
In these quilts that I am doing, I have used a white "sheet blanket" purchased at Blair for the batting. I have used two layers of this batting in each of them. I quilted some of the top block to the first layer of batting, then laid another piece of batting on the back piece of the block or strip and then did more quilting by machine on the top block catching all four pieces. I then do the 1/4" around the whole block.....makes it very stable.
When joining all of your blocks or strips, keep the bulk of your project to the left of the needle. You are able to fold and or roll whats to the left & right of the needle as needed. I use black plastic pinch type clips purchased at "Harbor Freight" to hole all my work. These clips have become my "best friends"..........Good luck with your binding.