Hmmmmm........where to start.
October. Don't go a day sooner. That place is miserable before that. I have been twice, once in the spring and this past fall and the fall was nicer, but in the spring, the trails are less stacked because the winter rains wash out the trail.
Plan on wheeling out there during the week. There are lots of guys that will show up just to show you around. I can make some "E" introductions.
From Alabama, the only good way to go is I-20/I-10 all the way to Palm Springs and then turn North. It was 1800+ miles for me from Jackson one way. I made it out in 2 days.
Possible stops on the I-20/10 route are: Las Cruces (1 day max) and Phoenix (2-3 days) Phoenix has 3 good areas to wheel. I can get you hooked up with heinz57 and Azrkcrawler for a good time there. Plan on wheeling on the weekend in Phoenix and during the week at the Hammers. The trails the BTG guys run are semi-secret so there is no traffic on the weeknend but the Hammers are crowded often time on the weekend so I suggest planning 3-4 days during the week. You can hit everything in that time as long as you stay in one piece. My group did the entire Hammers/Phoenix trip without any breakage.
Here is my trip report: http://www.pirate4x4.com/forum/showthread.php?t=623454
Figure 3-4 days out and 3-4 days back. That is a week of driving and a week of wheeling. Pretty much gives you time to do Phoenix and the Hammers. If you think you can/want to squeeze in more I would consider Clayton OK, Farmington or Moab, but I think your plate will be full with the Hammers and Phoenix.