I don't fly/book with America West, so don't know if their system is set up anything like the airlines I've booked with...
I've made reservations for myself and others, and I've found the important thing to remember and note (write down), is the confirmation number. It is usually the easiest way to find the reservation and/or print up the boarding pass. If the person flying doesn't print out a boarding pass ahead of time, it can be done at the airport--you can go up to an agent, or use the self-service touch-screen monitors in the ticket lobby.
Knock on wood, but thus far, I've never been asked to provide "proof of purchase." But that doesn't mean it couldn't happen.
Printing out your boarding pass ahead of time should preclude the airlines from asking for proof of purchase (a boarding pass should be an indication that the purchase was completed/paid). Printing your boarding pass early is also a way to avoid having to stand in at least one long line at the airport...but if you have baggage, it sometimes takes almost as long.
A couple of things to keep in mind. 1) Some/many airlines charge hefty fees for changes, etc. once the reservation has been made or ticket purchased, so be very sure of the flights before you commit. Tickets can also be non-transferrable and non-refundable, so beware (read the terms and conditions!). 2) Be sure to have the exact, correct name on the ticket/reservation--with current security, they WILL check the person's ID against the name on the ticket.
Remember, the above has been my experience, but the airline you ultimately select may be completely different, so the best thing to do is check with them. I've found it helpful to call the airline's toll-free reservations number to get answers to specific questions/concerns.