Become a lurker on this and other tree related websites. Listen to all the opinions, and get a feel for what the industry is doing.
Check out all the equipment available at various vendors, this will give you a good idea what people are talking about. Click on any of the ads at the top of this website, that'll get you started.
Read a lot of books: "what to do", "how to", and "why to do it" concepts should be firmly in your mind before you start investing in equipment.
Find some folks in your area that do recreational climbing, join up. Take a course, and get some good instruction.
There are lots of ways to learn, I suggest all of these before trying the method I learned by: buy a used old climbing belt and some spurs, buy a twist rope, and head on up the tree. That is the worst way to learn the trade, and really wouldn't be improved by buying the very best equipment available.
It's not the equipment that makes the arborist/forester/climber, it's the knowledge and the aptitude.