How long though will it take to pack boxes? If you can plan ahead a little now you can save time packing.
Important documents/papers for example, rather than pulling them out of a file cabinet or such I put them all in a zippered binder so its quick and easy to grab. It even has a pocket that my backup drives fit in so I don't have to pack and carry those separately, I just made it my normal procedure to store there when not running a backup.

Identical boxes has always been one of my goals. I like Rubbermaid tubs myself, they seem more durable than others and can be had in a couple colors if color coding is something you'd find helpful to sort contents.
Though I will admit, that the vehicle you are using to transport can definitely have an influence on your decision as I see pickups and vans being more useful for tubs rather than others.
I guess it has to do with how much stuff you want to take too.
I started with cardboard boxes ....cheap and readily available paper boxes from work that got thrown out if I didn't take them home. You can waterproof them some with matt clearcoat paint with helps durability, but I found myself reinforcing them to take heavy items and with money less of a concern switched to Rubbermaid.
I like milk crates too ...especially for transporting stored water as well as being able to stack it in an orderly fashion.
For anyone that's moved very often, like sized containers is the way to go.
Customizing containers to hold specific prep items and gear is my next step ....everything in its place helps with inventory and locating items.
Still have some 25 yr old paper boxes with segmented compartments for storing PVC sprinkler and plumbing parts. Makes finding stuff super easy. The tough thing with camp gear and such is picking what I'm gonna go with and not changing my mind when I find something I think is better so don't have to rework my compartments.
But hey ...having yer stuff packed up in something and all in one or two places ready to be loaded is REALLY, the first step.
Polishing the apple can always come later.

+1 on the rubbermaid brand. Relatively water resist and rustproof and a bit stronger than the rest

I have checklists for packings. Each list includes items/tasks sorted by person responsible, priority, beneficiary (son's diapers does not benefit the cat), and location of item or task. Ideally, I'd say 45 minutes from alert to full houehold evac, but it's more like an 90-120 minutes.

Copies of important documents, computer backup, and disaster related documents (i.e. pet friendly hotels, evacuation shelter locations, maps, etc.) are already prepacked in a waterproof bag.