This is rather like asking, "What do I need to get started as a mechanic?" and hoping for a quick, simple list. It's a bit more complicated than that, which is why there are so very many posts and threads about each single aspect of tree work on the arborist forums.
It might help to make a short list of the items that you know you will need, and enter them into the search function on each of the sites you use for your research. I'd start with the most obvious stuff... climbers/gaffs, lanyard/flipline, PPE equipment (gloves, climbing/chainsaw pants, helmet, climbing boots, etc.), tophandle saw, handsaw, saddle/harness, throwline... before you move to climbing rope systems. By that point, you'll need to know how you plan to access the trees, and how you want to work them. SRT for access, DdRT for work positioning? Friction hitch based systems, or mechanical multicender systems? The ropes and hardware needed vary tremendously, depending on your decisions. Will you use a long lanyard for secondary climb line, do you need a steelcore flipline, etc. It just goes on and on, which is why there is no single post on the forums that says, "This Is What You Need" because the post would be 200 pages long. And that's if you left the whole issue of RIGGING out.
I'm not trying to be a smart ass, and I'm certainly not trying to discourage you... just sayin'... the amount of stuff needed, and the cost of it all, is daunting. You have to start with a short list that will get you into a tree, and research that small number of items very well, to ensure that you're not buying the same type items over and over, needlessly. Some of that will happen, but you can at least minimize the chances of wasting any time or money if you get a lot of opinions about each item you need. Or, simply find the right area on the forums site, and start reading. Again, the search function will help.
I think your first considerations might be: Climbers, Lanyard, Harness, Helmet and try to get those ones out of the way, because the options are many and those items will get you into a tree for removals. That would give you a core from which you can move outward.