If you've never had much upper-body strength, I'd allow longer to build up to handstands and walking on your hands. If you'd like a specific by-May goal, maybe look at how many pushups (full-length and from your knees) you can do now and pick a goal based on that.

I've also never been to a gym that was much good at actually helping people improve flexibility. Most of what I know I've learnt from my own experience, and reading Kit Laughlin's books