Lowes and Homedepot offer builder grade plywood, great for the every day contractor but not so great for lasers. Also if you check the thickness its not true 1/2" plywood. I would talk to a few lumber yards and see what they have instock and what they can order.
As I stated above, a go to plywood for Lasers and Routers is Baltic Birch - Its offered in a verity of Thicknesses and is available through out the US. We go through pallets of it each month and it always cuts well, We get a few hard spots every so often but what do you expect its from Russian :-)
Monograms are a pain to cut, make sure you cutout the middles first and then make the second order the outside.