I would start by reading this thread by
@Batto who actually did start his own animal collection and talks about the process. I would say, unless you know some billionaires that are willing to fund you, the idea that your going to create a huge zoo/amusement park isn't very likely. Batto says as much in his thread, but creating something small and building upon that slowly is possible. There are many small privately run zoos around, but they all have taken time to get to where they are now.
How to found a zoo [Welt der Gifte]
That being said, I see you posted a very similar topic before and didn't get much response. I don't think there's going to be to many people here that can tell you how to start an animal theme park like you describe. For one, there just isn't that many parks out there like what you describe for a reason. On top of that, the people who did start those parks probably aren't on this forum. If you are truly set on this goal it will take a lot of hard work and determination. The first step would probably be to create a full blown plan that you can then bring to investors that would be interested in funding such a project.