If you go the route of using an external recorder, PluralEyes might be a good plug in to invest in. It's super helpful if you have a ton of footage.
Vimeo on demand is an option, but the cost could be out of your budget
I think the 150-600 should be a good starting point. Afterwards you'll figure out what wildlife you like to capture and what focal lengths you use the most. I think the only other thing you would need in terms of equipment is a very sturdy tripod because if you're at 600mm it's going to be hard to track wildlife.
Consider what you're looking for in a school. Some are theory based while others are more hands on. Also think about what position you want to have once you leave. Do you want to be a DP, editor, etc. Once you have both of those things figured out you can start looking at which school would suit you the best.
I'd say a good number of best picture nominees have fairly small budgets, like around or less than 50 million. Here's 2008:
Juno: 6.5 million
No Country for Old Men: 25M
Michael Clayton: 25M
There Will be Blood: 25M
Though, there were fewer nominees that year. I would say that most of the 2015 movies had fairly small budgets as well.
I think it's important to define what sort of filmmaker you would like to be. Director, DP, editor, writer, etc. That decision generally will change the best route for you to take.