I work at an independently owned pack and ship/mail box center, and we ship bikes all the time.
The best thing to do, to avoid being charged for a bike sized box, is to see if you can pick up a used one from your lbs. All of the packing materials that would do an adequate job of protecting the bike and its parts, otherwise, are best purchased from a place like where I work. Look for independently owned pack and ships, because the kids at kinkos and the ups store don't have A CLUE about how each shipper honors insurance, the best way the pack things that mean alot to people, how to button their shirts, or how to pack things to each shippers specification of what can be reimbursed and what can not.
The more you pay for shipping, the less chance their is of someone throwing it (and trust me, they will throw it.) from truck to truck to truck to truck. I always say, if you can afford an air service, go that route. Its gotten entirely too pricey though. 3 day select UPS, or Express Saver with FedEx are good compromises between cost and safety of your package.
Now with packing...In order for FedEx or UPS to honor insurance with things like wheels, they will need to be double boxed to this spec: Form fitting box with enough packing material (peanuts, etc.) to keep wheels from moving, then placed in ANOTHER box that allows for at least 2 inches of firm packed peanuts ON EACH SIDE of the original box. I, personally, would NOT trust wheels to be safe packed with the frame unless the box was specifically designed to carry both the wheels and the frame. With things like forks, I dont see a problem wrapping them in bubble then folding a cardboard shield around it and sticking it in the frame box. Cardboard shield, with enough room around it, is essentially the same as a double boxed item.
Really the best thing to do to ensure its safely done is take it to an independent shipper that is not a corporate entity. The people working there work hard against their name brand competition and are generally more knowledgeable and helpful because of it. But its like finding a good LBS, it might take a bit.
Hope that helped some.