More info on the archer deer there?
Take hunters safety right away when you get there, point for every species for life.
I've spent a lot of time down there from the Feb.-April time range working. The fishing is spectacular at that time of year, Bartlett, Pleasant, Roosevelt, Apache, Alamo all very good. Good as in up to 100+ fish days for stripers, white and yellow bass, largemouth and smallmouth bass, crappie, etc. I fished nearly every weekend I worked down there.
Also helped a couple buddies with spring turkey down there as well, its pretty good hunting and the tags don't seem all that tough to draw.
Personally, I would make sure I drew and hunted coues deer every year. It's the one fairly unique species that you can't hunt in a lot of other states. They are WELL worth the effort, very challenging and one of the hunts I look forward to the most in AZ.
Elk hunting is excellent and I would think if meat is all you're after either the general seasons or cow seasons are pretty easy if you aren't picky.
I would also take advantage of the wing shooting primarily doves and quail, its very good.
Would also be a good time to bag a few javelina, custom built for short range weapons and also another unique species. Predator hunting is also very good. I see bobcats nearly every trip down there, including the most recent trip this past December. I would think with a semi-serious approach you'll get grey fox, bobcats, coyotes and very likely a lion.
Don't dread it, embrace what the State has to offer...