Are there only drawers in the vanity, or does it also have a cupboard space? If no cupboard, then you have to fit the things you have into the drawers. Personally, I like bottles and other tall things on a lazy susan in a cupboard under the sink (where opening and closing doesn't knock them over, and where I can see things easily), and then smaller things in drawers. But I'd still find 3.5 inches a bit shallow. It also depends on what your other storage is -- i.e., do you need to keep your toothpaste and make-up in there, or is there a medicine cabinet for some stuff or a counter organizer. I think three drawers is probably the right depth if you can make it work, but if you know you want bottles, then make them include one at 10 or 11 inches deep. (Alternatively, you could have a deep and two shallow on one side, and three medium on the other, which is likely to cover most of your needs. Symmetry can be stifling.)

Shallow drawers are more practical for a vanity and vanity products. Everything gets laid on its side and is immediately visible with no digging around. As long as you have 1 deep drawer for a blow dryer, all the rest as shallow drawers will give you the most organized storage.

There is a cupboard under the sink, but we were thinking of using that for cleaning supplies, plus there will be plumbing down there. There is no medicine cabinet.

I don't have measurements handy, but in the attached pictures you can get a sense of the depths we chose for our banks of 3 drawers. Deeper drawer for hairdryer and brushes was necessity for me. Frankly we have not yet managed to fill all drawers. But in all cases we did a shallow one with 2 deeper underneath. Top shallow drawers I use for makeup, toothbrush-toothpaste-floss, eyeglasses, etc. I do not mind some things on counter for convenience/daily use, like moisturizer.

The drawers by the tub, with linen cabinet above, we use for first aid - bandaids/drugs etc - and also travel kits, things we don't need daily but still get good access to.

If you are looking to to stand bottles and spray cans in at least one of the drawers, did you ever consider over the counter storage? I bought a really neat makeup, hairspray, everything organizer right here on Houzz that gave me a lot more room. :) Here is the link https://www.houzz.com/products/luxury-beauty-case-and-makeup-organizer-prvw-vr~52523042?lid=37731778