Start by getting the book Tree Climbers Companion and the Video from Treeman (TCI) about Basic Tree Climbing Instruction. By reading the book and seeing the demonstrations from the video you will get a better sense of what you definitely need to have and to get it from. After you take care of that we can suggest a basic gear set you will need to buy to get in a tree safely and have some fun climbing trees.
Oldtimer, Tree Climbing In Austin
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Then here's to the oak, the brave old oak,
Who stands in his pride alone!
And still flourish he, a hale green tree,
When a hundred years are gone!
--Henry Fothergill Chorley, "The Brave Old Oak"