Some tips for handstands: I think everyone's advice to practice them with a wall/pole is great for building the strength needed. It is a lot of shoulders and core. Once you are comfortable with the strength, and want to try them free, this is the number one fix for balance for people not trained in handstands. you NEVER "kick" into them. your arms, torso and leading leg make a straight line that does not break so as you bend down to the floor, your leading leg is lifting at the same rate. Really squeeze your core to keep everything in a straight line. ALL OF THE PUSH COMES FROM THE LEG STILL ON THE FLOOR. do not use your top leg for momentum.
Practice baby ones on the floor. Assume the starting position (like down dog with one leg lifted), squeeze your abs and your glutes, and bend the knee of the leg still on the floor and do tiny pushes where you straighten the knee and point the toe in the air. As you get comfortable with this, push more to get into what I call an "L handstand", where your body and vertical, your top leg is straight like a true handstand, but the bottom leg comes out parallel to the floor so your legs are in the letter L. Be careful to not allow your top leg to fall over your head, so you are in a split. Due to physics, it is really difficult to hold the L handstand for any length of time. It is also difficult to fall over backwards.
Once once your L is controlled, then you can attempt bringing the second leg up. Try them about a foot in front of the wall, so if you fall, you have something to catch you. or with a spot. Also, learn several bail out methods (twisting out is safest, but you can bridge and forward roll as well.
Let me know if you want a video tutorial!