Hi Rich,
Glad to hear you're ready to try cutting.
With most blades, and especially with Mike's blades, the thinner the wood you are cutting, the more aggressively the blade cuts. If your blade is cutting very aggressively you will find it somewhat difficult to control. I typically cut with 1/8" BB Ply for my portraits. I find it allows me to use most store bought frames with no trouble. 1/4" can sometimes be a little thick and I will need to make a custom frame.
When cutting 1/8" material, you will soon realize that your blades move through it like a knife through butter. I usually turn my saw speed way down if I'm cutting a single piece. Normally I stack cut 4 to 6 pieces giving me a 1/2" to 3/4" piece of wood to cut through. This allows me to maintain very fine control on the straight blades. With spiral blades I do not have this problem.
As for the background showing through, as a general rule it is easier to see if it is closer to the surface of the cutting, so on 1/8" material it will be very easy to see. You will need to determine just how three dimensional you want the piece to appear. If I'm framing a piece I go with 1/8". If it's a wall hanging I will use up to 3/4" material to give it a little more dimension.
Hope this helps. Barry