A couple of answers....Yes, quilting your fusible fleece to your fabric will make it a bit more sturdy and alleviate the problem of the fusible becoming 'unfused' and shifting on you. Not only did I quilt my outsides and lining, I also quilted my pocket pieces both for the inside of the bag and the outer pocket. On my purse, the botton fabric was a vertical stripe...I could have just followed the stripe, however, what I did was lay out my piece on my mat and draw a line from top left to bottom right on the 45 degree angle. Then, I turned and did the same thing so I had intersecting angles. Stich first on that line and then I used my quilting guide bar to stitch 1 1/2 inches on either side of that intial line until it was quilted. For my floral upper purse fabric, I free-motion quilted.
As far as handle length goes...you can certainly make them any length you wish. Simply cut yourself another stip of width of fabric and fleece and cut them to the length you like. I think handle length is just a matter of personal preference. If I remember correctly, after cutting off the piece for the loop, I had 34 inches which cut in half allowed me to have 17 inch handles. I made the mini-Bow Tuck bag. I am not sure what the length is for the regular Bow Tuck bag.
Regarding fabric choice...I used cotton fabric I purchased at my LQS...it is very nice to work with. Hope this helps you a bit!