A lot depends on what you plan to keep in the drawers. You could have graduated depths like 3", 5", 7" and 9" for overall usefulness. If you plan to have small storage boxes in the drawers, then their height plus an inch or so. If they are just for notions, then shallow drawers would be better; pattern books with their spines up would need more depth.
The dresser in my studio has maybe 7" drawers and I keep bolts of fusible web in one, rolls of Japanese papers in one, things that can be stacked without needing to 'dig' through them to get what I want.
Hope that starts you thinking. Have fun in your new space!