When I sew on the leather handles I use the silks used for cross stitch, this way I can match up the colour to the leather handle perfectly. Also,I don't seperate into strands I use it as it comes, doing back stitch all the way round.
I do a double back stitch in the last set of holes of the 'horseshoe' then take it behind the fabric and do another back stitch over the stitches at the begining of the 'horseshoe'. I sew the handles through the outer fabric and interfacing, if the bag doesn't have any interfacing,c ut a some pieces to go behind the outer fabric to sew through - this just gives a bit more strength to the bag.
Everyone will have their own way of doing it, but I just thought I would tell you how I do it.