Set the z depth to whatever you want up to .25 or 1/4". I'd recommend no more than 1/8th inch (0.125) as a guideline, especially if you're doing extensive carving. Note that plywood is made of layers, so your cut area may be darker than your surface, and would stain differently. In carving something this thin, I ALWAYS use a sacrificial board underneath the project board, depending on your preference and project you can either use dual sided tape or (my preference) is put a screw in each corner and cut off the excess wood after the carving is done on a table saw. I have a 1/2 board cut to 13 x 19 that I use like this, I drill a pilot hole for each project depending on the wood size and clamp down on the sacrificial board instead of the work piece. The screw method helps straighten out any cupping or warping your board may have, often seen in thinner boards.
Heavy carving or fast speed during carving can be a problem with double sided tape, though I've seldom had problems - it has come loose once. Clean boards and good tape are ok, even on cut through projects.
Either bit will work, depending on what scene you're carving. 1/32 is good for lettering, 1/50 for detail. Low speed is probably preferred.
Here are a couple of 1/4 oak projects I did as a cut through (z = 0.26) with a sacrificial board underneath and held down with double sided tape: