At a minimum?
A climbing rope
A saddle
And a lanyard/flipline
That would allow you to climb a tree using a doubled rope technique, now commonly called moving rope system, and also to tie in twice while making your cuts.
It's highly recommended that you add PPE (helmet, eye protection, ear protection, etc.)
Additionally:
A throwline/weights would make setting your climb line easier in some trees, and possible in others.
Spurs (only if you're doing removals) can aid in movement throughout the tree.
Some companies offer kits. Browse Treestuff, SherrillTree, Baileysonline, etc.
After that, it's up to you how much you want to spend and what system/gadgets you'd like to use. There are plenty of threads on here and videos on YouTube explaining the different systems and equipment. It's a fun skill to learn.
One more thing: buy,
read, and re-read The Tree Climbers Companion by Jeff Jepson. Then, once you do begin climbing, always practice everything low and slow before doing actual work, to minimize the chance of injury.
P.S. Topping trees is typically not recommended