Sugar/hard maple, hickory, and white oak all make very good backings. I keep all of them here. If I had to make a trilam with the three of them, I'd use maple for the back, white oak for the core, and hickory for the belly. But they're so close, they could be used in any combination with a few adjustments.
When I go to the hardwood store, I look for all three of them, plus cherry, osage, mulberry, walnut, ipe, all sorts of stuff
I look for wood type, but clear wood, ring and grain structure make the ultimate decisions for me. If you don't see something you want, ask. The last time I was at a big hardwood store, I told them what I was making, and that osage is what I really wanted, and he told me they had some at their big warehouse several miles up the road. He was supposed to call me... never did.