I like to use the solid core 3/32" thick project panels I get from HD. I like their Maple but they have been out of stock on the 5/32" thick Maple for some time now. I'm low on these panels but HD does have Birch panels in this thickness. It is almost as pretty and nice as the Maple, just a slightly different color. It is called Birch, but I have know idea if it is "Baltic" birch. I just placed an order forthree boxes (30 sheets).
Currently I do have a fairly large number of 1/8" BB ply, but I dont't use it that often. I also have good stockpile of 1/4" material that I mostly use as backers including: BB ply and the solid core Walnut, Red Oak, Mahogany, Cherry and Maple panels as well.