You are correct, there are 100's of place to stop....not sure which way you plan to travel from Alabama, I-10, I-20 or even I-40. Just remember if you go I-10 or I-20, a big part of one day will be driving through Texas and not really some of the more interesting parts - . That said, if you go up via the panhandle, might plan a stop at Palo Duro canyon...good camp ground, just south of Amarillo, from there I-40 into NM and then North on almost any road to I-25 makes a really nice drive with lots to see...think I have driven them all at least once.
I-20, I-10 (they meet up near Van Horn) is pretty barren until just West of Pecos (there is a nice stop in Monahans, at the Monahans Sand Dunes - another state park), then a turn North from Pecos will take you to Carlsbad and White Sands. Good camping near both of these as well.
Maybe a loop, from Carlsbad/White Sands the North to SF back to Amarillo would be nice. Lots of windshield time though but lots to see as well. Temps will be a bit more comfortable for camping though.
Most of all, have a blast and shoot lots of film so we can all enjoy your trip too