If you've got a strong back and cushy knee pads I'm sure you could do the stone work. It sounds as tho you are most afraid of the prep work - leveling and not messing up the drainage. Has drainage been a problem? Are you concerned because of putting in the raised beds or is it the whole area? For a patio I would think you would want it almost level.

If I wanted flagstone, I would not go with pavers. Think about hiring a laborer/helper to rake all the gravel to the bottom of the flower beds, fill the flower beds with top soil before or as the stone wall is built and to make-ready (with stonedust and a little sand) the patio area. Unless you use small flagstone I'm sure you will appreciate some help hauling the stone.
Hopefully, since you are in Arizona this is a late fall/winter project.

Ironically, you're not a newbie compared to most people who take on this sort of project. You also fall into the category of people who will probably be most frustrated by having contracters, as you probably have pretty specific expectations about how they should do it.

I agree that the site prep is what you sound most leery of, and it isn't rocket science. Get a book on laying patios that explains site prep, levelling, and base material selection (I have one I like called Patios and Walkways, do it now do it fast do it right, by Taunton Press), and you'll see that it's well within your reach.

Regarding drainage, think about where the water comes from, and where you want it to go, and slope the patio accordingly. Flagstone has gaps that the water can soak in between too, and you're not exactly in a high rainfall area either, are you?

If you want flagstone, you won't be happy with pavers.