OK...I do mostly portrait type cuttings. My procedure is to 'stack cut' any where from 3/8" to 5/8" thickness of stacked BB plywood.
Most often it is 1/8" pieces with an ocassional 1/4" piece.
When I look at my pattern I will go to my stack of wood and try to select wood that has a grain pattern that is in keeping with the pattern itself, either vertical or horizontal and fits with the theme of the pattern. Sometimes I will 'reverse' a piece in the stack so that the final cutting will be a mirror image of the cutting (put the back side up in the middle of the stack).
The bottom piece of wood is always what I consider a 'throw away' piece since I use only 2/0 spiral blades and that piece will have the worst of the 'fuzzies'. Most often I am able to sand and file those 'fuzzies' off and still use the piece (a bonus, if you will).
All pieces are sanded to at least 220 grit on the 'face' and 150 on the back before starting.
After cutting I soak the pieces in the famous BLO mixture for at least 10 minutes and then allow them to dry 12 -24 hours. The backer I use is chosen the same way as the the wood itself and is in keeping with style and subject matter of the portrait. It may be stained oak plywood, heavy 'scrapbook' paper or frabric, mostly felt.
When making my 'stack' I simply clamp the boards, tape the edges with painters' tape apply my pattern to the top board with 3M77 spray adhesive and then cover the whole pattern area with packing tape.
In the cold months, like now, I bring my precut plywood INSIDE and allow it to come to room temperature before making the stack and applying the pattern. If I don't finish the cutting in a single sitting I bring the piece inside to stay at room temperature until I go back out and heat up the shop and start cutting again. This prevents wide temperature swings of the wood.
It works well for me!
~~~GB~~~