In regards to submission,
PCGS: They are very accommodating in regards to submissions. You can either have the coins in capsules or flips. They even provide the 2.5x2.5 flips if you don't have them. You do not need to label the coins or rubber-band (they will rubber-band it for you), according to my experience with them. If you have them in capsules, you can either put them into the flips they provide you or they even let you submit them in the capsules (they have you put the coin in the capsule in the flip). If you want the capsules returned, they can do that for you too (for no extra charge). The representatives are very helpful throughout the process.
NGC: I do not have direct experience with drop-off submissions but have used their on-site service. They accept their coins in capsules or flips, but charge a $3 fee to have the capsules returned (their "return mint packaging" service). Their representatives are also very helpful throughout the process.
For both, I do not believe you need a box (the beauty of the 2.5x2.5 flip dimensions is that it also fits into their usual slab boxes and probably the other slab boxes they would use). I am almost certain of this for PCGS but am not entirely sure with NGC. I also believe you can submit them in either capsules or flips. Last, I know you do not need to rubber-band and label them with PCGS, but am not sure about NGC.