Ross, as mentioned, buying online is easy. Arizona has no "gotchas", so order away.
If you are buying through one of the larger online retailers, there is usually a dropdown menu in their "ship to" page on checkout that has a list of all the FFL's they currently have on file, and you order in confidence that an FFL on the list will accept your transfer. If it's a smaller shop with a lest robust online ordering program, you'll need to have your FFL fax/email a copy of their license to the shop first... which means you need to call/email the shop or go in.
If you can buy a gun online for $500, plus $15 for shipping, and another $20 for FFL, you're looking at $535 in your hands... this is a good "deal" if your FFL is selling the same gun for $550+tax.
Counterpoint: Particularly when it comes to their gun hobby, lot of people place $$$ a few ticks lower on their list of buyer decision-making than with other items. LGS's (local gunstores) should be supported. They serve the industry in a far more significant way than simply being a place you can buy stuff. Even if it's a few dollars more, money spent at your LGS is almost always well spent. If I buy a rifle online, I try to buy my accessories in the shop where I pick it up... all my reloading supplies (when there are any), scope, ammo, case, etc. I want my LGS to be there for my kids, and it won't be if I buy everything online.