I am working on my handstand these days. Headstand in the center of the room is no problem and I can hold this for several minutes if I want to do this.
I see many people doing a handstand throwing one leg up at a time and then balancing. For me I am going the same route as headstand and am tucking my knees in slowly and then lifting. I am almost there. Question is this. Is there a proper or preferred way to do handstand? The tuck method just seems more normal for me and more controlled.
Its perfectly fine.
Just make sure you use wall first behind you so that you can refine your posture instead of holding with fear of falling. Generally taking one leg up first with other leg half bend helps a lot in terms of getting balance.
Here you see a video of handstand and how to do it after a moment of letting the body go.
Hand balancing is an entire art of its own, with many variations and approaches. Typical ways of entering include split leg entry, jumping with bent knees and legs together (tuck up), straddle-up, and pike-up. There are also many different ways to balance once up there. I'd encourage you to practice different variations.
If you are interested in developing your handstand, classes are available in many places. I come from acroyoga, and many there have a HS practice.
I teach acroyoga myself, and have been practising hand balancing for the last few years.
Cheers