I'm looking to become fit in my upper body without having to go to the gyms. Right now I'm working on my pushups. I can do 30 normal pushups in one go, if pumping as fast as I can. I'm 6ft and 160lbs. I've switched to wide pushups and now do a combo of wide+feet elevated pushup. I can maybe get 15 in one go with this setup. 

I try to work on my pushups 3 times a week, each time I do 5 sets each in the teens range. My goal is to get my strength trained enough so that I can do one hand pushups, which I can't seem to do yet. I hope that by adding additional difficulty to my current pushups I can develop the strength to do one hand pushups.

After I become strong enough at one hand pushups I plan to start training with those instead since I essentially double the load on my arm and chest used. Eventually, after getting good at one hand pushups, I can hopefully handle working with handstand pushups. I know that core strength is required as well, but I can start off handstanding next to a wall, so my core wouldn't be overwhelmed. 

Does all this sound like a good plan for reaching handstand level strength?