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Also keep in mind that wood swells and shrinks dependent on humidity/moisture etc. so a difference of .5mm might well be the difference in season or location
Even acrylic (which doesn’t change that way) has an “acceptable” amount of variation in thickness
In my experience “Revolution” plywood is the least expensive out there and can be found at Lowes or similar. but for actual wood you might have a local specialist that will not charge shipping, or an E-bay seller with a smaller selection but reliable folks with a good selection there are a number… Thin Scroll saw wood pricing sheet, Green Valley Wood Products Baltic Birch Plywood - Woodworkers Source
Hardwoods, and plywoods, won’t come finished and most won’t come pre-masked. Unless you’re making purely 2D things, however, the pre-finishing is usually a bad thing and masking is no big deal. For that reason I pretty much only use non-proofgrade hardwood.
I don’t have a preferred supplier yet, but be careful in saving money. You may find stuff advertised as “sanded to 120 grit” to still have a bunch of saw marks or other deformities. I’ve been able to work around any bad pieces, but you certainly don’t save time. And I’d be surprised to find consistent thickness. Be prepared to adjust designs for thickness, cut large and sand flush like evansd2 does with his finger joints.
I have found that unless the wood is ultra hard a rough sand is little issue especially if I am doing a deep engrave where that surface goes away anyway, Even otherwise a 400 grit belt sander makes short work of any of it.
We have a store here called Macbeath Hardwood - I buy sheets of maple ply for a very reasonable price and cut them down myself. Perhaps you have something similar close to you?
This past holiday season I purchased and cut several hundred 1/8" boards from Lasered By The Creek. Not a single glue pocket or void. Cuts very nice and clean. Also has a proprietary wood core instead of MDF which allowed me to cut faster (ie. speed 195) and since it cut cleaner I had less maintenance cleanings between cuts.