I have planted quite a few thousand trees. Used a planter pulled with a tractor where the land permitted. Never tilled first. However I would reinforce the comment bout following the machine and heeling them in real well. Leg gets tired, but worth it to make sure the roots are not hanging in a pocket of just air.
For hand planting I always used the tool pictured, and another one without the tomahawk end. Figure out your spacing and just pace from one tree to the next one. Womp that pick in the sod, pull back, stick in tree, heel in, pace to next one. I've had good success doing this. If you like exercise, and can keep it up, 400 trees a day is not unreasonable.