I found that the easiest way of learning the handstand is to walk up the wall (with your back to the wall, put your hands on the ground and walk your feet up), rather than kicking your feet into the air. It’s slower and more controlled. - Of course, this is only an opinion and if it causes you any discomfort, don’t do it.
As for learning to do an unassisted handstand, the best thing you can do is to simply practice the assisted version, over time gradually stop using the wall to stabilize you. This will be as good or better than anything else at training the necessary strength to do a handstand.