You will need compression spirals when using birch ply to stop break out on the cross grain. Preferably an up down cut too to stop break out on both face unless you use a matrix bed with a spoil board, then just use a down cut.
I've just finished machining a kitchen for a customer which was totally in birch ply but the problem was I was getting rippling on the edge from the layers, and that was with a fresh cutter too so would be interested in how others have solved this.
Try the Chinese cutters for your smaller sizes, they usually are ok, may not last long but for the price. Anything over 10mm diam I would say get some better quality ones.