Priority Mail with confirmation is my preference; if I'm shipping anything OOP/HTF, I'll also spring for insurance. I've never been disappointed with Priority Mail; even with the recently raised rates, I think it's worth it. Delivery time is quick, and I want my trade partners to get their stuff fast, because I can't stand the waiting! As for the confirmation and insurance options, I simply like the peace of mind.
To pack, I usually use the Priority Mail shipping boxes that come in varying sizes, right down to those little near-deck-size numbers. When my guy gets computer parts through the mail, I have those boxes to use. If not, mailers are indeed inexpensive to buy, and I can still pack decks as securely as a sturdy box.
I did have a bad experience when I first started trading, where the deck I received came to me via a mailer, and the cards were floating loose inside. So I've learned to be sure the deck is wrapped in bubble wrap, plastic wrap or at least tissue - whatever will keep the flaps closed without putting tape right on the deck box.
It's important to me that nothing moves around or rattles in the package once it's closed, so I like oodles of bubble wrap around my outgoing decks. Oh, and plenty of packing tape on the outside. I'm talking lots and LOTS of tape. Basically, when I ship decks, they tend to be hermetically sealed and prepped for an all-weather survival trek.
It's not even remotely necessary to go so over-the-top like I do, but even if I ever stopped going mad with the packing tape and bubble wrap, I'd still ship via Priority Mail.