Since you're handloading, any of the three will work since you are able to load the cartridges down. I loaded some 30-30's for my 10 year old daughter using 150 grain softpoint's. I kept the velocity down around 1500fps, so the recoil was pretty mild. 75-100 yards is about as far as she can shoot accurately, so the loads worked very well.
I like the 30-30 for simplicity, I own both the 7x30 and the 30-30, and have owned a 30-30AI. I always come back to my 30-30 since it's easy to load and does not seem to be very picky about bullets and powder. My 7x30 and my 30-30AI seemed to be a little more finicky. Also, for my kids, I can load the flat-nose and round nose 30 caliber bullets that were designed for the old lever guns, they will perform at the reduced velocities.