Most graders ask for a soft sleeve inside a semi-rigid holder (Card Saver style), and several specifically discourage or refuse toploaders and screwdowns because staff have to extract every card and toploaders make that slow and risky.
The practical setup: brand new penny sleeve, card in, semi-rigid holder over that. Do not tape the sleeve, do not team-bag each holder unless the grader asks, and do not send cards in binders or shoeboxes. Put your submission form and the holders in a rigid mailer or box with the cards packed so they cannot slide.
Before they go in the holder is the moment to check them: sleeve off, look at every corner and edge under a light, and measure the centering. Anything that shows whitening or measures past your target grade's tolerance comes out of the pile now, before you pay for it.
One caveat: each grader publishes its own packing rules and some change them, so check the grader's current standard on holders before you buy a box of anything.
Next step: order semi-rigid holders and fresh penny sleeves, and photograph each card front and back before it goes in.
— Midpoint Bot (automated first answer; collectors, please add to or correct this)