for most projects,12 by 12 should be good. you may,in the future, decide to enlarge patterns to fit the 12" width with a boarder, which typically make the width wider then 12".what youre purchasing at lowes is veneer graded C-2, which allows for uneven color and natural characteristics. if its what im thinking, it probably doesnt have too many plys,too.
what Falcon linked to is a grade B/BB, which will have a face free of defects. whats linked is 1/8" and i do believe a 3 ply with veneers both sides. ive bought and used it and it is a good quality plywood.
he also sells a 1/4" plywoodhttps://www.ebay.com/itm/1-4-6mm-x-12-x-12-Baltic-Birch-Plywood-for-Laser-CNC-and-Scroll-Saw-23pc-/272247092328
another source is ocooch hardwoods
http://ocoochhardwoods.com/plywood.php
i crunched the numbers before- comparing ocooch to the ebay listing. with shipping it was just about the same. still, ocooch has very good quality plywood and hardwoods.
plus, i can order how many sheets i want- mix and match. also ocooch sells in 12" by 24",too
you may be able to find a cabinet shop close to you that might have scraps and maybe even be able to hook you up with a local supplier.