As far as whether to learn Axe-Edit or front panel first for editing, I'd say it boils down to how often you're gigging out with the Axe-Fx.
If you're gigging out every few days, definitely learn how to use the front panel first.
If you're mostly playing at a home studio, I'd stick with Axe-Edit for a bit, until you get comfortable with the concepts. When I first started, two or three Axe-Fx's ago, there was no Axe-Edit, and it was exponentially trickier to get all your eggs in the right basket, and saved, exactly like you wanted them to be. Axe-Edit graphically shows what's in the patch, what's on, and many of the parameters are handy on the front page of whatever amp/cab/effect you is open. It's a piece of cake to make a preset, see what you've got going, and save it, or rename it. Scenes are easy to pop back and forth, to see what's happening there, if you start getting into using Scenes.
The first year or so I had the Axe-Fx, I kept gigging with my analog rig, and using my Axe-Fx in home studio. This allowed me to learn it inside and out, before embarrassing myself. Now, it's just the opposite - I will rarely drag the whole kit and kaboodle, when I can take the Axe-Fx, a FRFR or two, and an MFC - good to go.
If you're gigging out a lot, and want to start using the Axe-Fx right away, I'd go with what AndyOrr said, and learn front panel first; otherwise, that's not the route I'd choose. YMMV. There were a couple of uncomfortable moments onstage, when I'd have to make a change that I had a brain-fade, and couldn't recall what to step through to get to a certain parameter. No biggie, if you're home, but gigging, this can be a huge distraction, if you don't know your way around the panel settings. It gets to be second nature after a bit, but can be a little daunting, at first.
At home, I still prefer using Axe-Edit, instead of front panel, because of the large amount of information that's graphically shown, and the ease of changing several parameters in a screen; you're just a bit more limited in what you can get to without stepping from screen-to-screen when working with just the front panel.
A caution, though, it's always good to not work back and forth with in a preset from panel to Axe-Edit - some things can get boggled in the process. Stick with one or the other in a sitting, and be sure to save before switching back and forth within a preset. If you're using the latest firmware/software, they usually pause you if you go to front panel, and you hit F8 to return, if you're working with Axe-Edit, and jump to front panel. Try to avoid this, though, as it can be glitchy. I don't "think" it's ever hung me up, but you never know.