Even though I’m not a known fan editor, I’ll dive in to give my thoughts, which I’ll keep broad enough so that it should be of (introspective) use.
First, your wanting to do THIS project is biting off a lot. Before anything, you may or may not know that many people hate the straight disc releases of LotR (and I haven’t read the books, but I doubt they said everything was tinged in green everywhere all the time). So, right off the bat you’ll probably want to edit (color) someone’s restoration (ala Dr. Dre’s or one of the similar…) This is a bit perilous in and of itself in my opinion. What if you are almost finished with your edit and Dr. Dre releases a new version of his color revision release that you and everyone loves more than the one you used? You might be able to just swap the master file for your edit work, but maybe not, and if the latter then the image of all your work might suddenly nag at you in a way forever after after you put all that work into your edit(s). 😦
I’ve been helping a new fan editor who took on a big project, and it’s actually been going well as the guy is quite talented, everything he went to address, I agree with, etc. Still, he’s spent and ungodly number of hours on his project and he still isn’t done yet. I think it will be worth it when he gets to that finish line, but I’m bringing this up to roundaboutly ask: If the edit you dive into a) doesn’t turn out well enough because you’re too new to this b) it does turn out well but you ended up spending piles and piles of time over months/years to finish it, would you be okay enough with either of those being end results of your work?
Lastly, I know that people have done some “closer to the books” edits of LotR. Sadly, it’s pretty hard to get a lot of older edits, or even newer ones, so I can see from that viewpoint it might just be better for you to try to do yours yourself and learn about editing and more in the process instead of getting on the begging wagon…but just in case you think 100% the ONLY way you can see a LotR trilogy is do to the edits yourself, I’m pretty sure that’s not true (but maybe those edits, you believe you could do better, and maybe you could!😃).
If after reading all the above you’re still wanting to dive into it then your big step will need to be to pick editing software that fits your needs/style/budget/equipment. Da Vinci Resolve is rather the rage right now. I haven’t used it, but it has a very good free version, and it’s very powerful, but if you have only an old Win 7 machine then you won’t be able to use it. There are many other editing programs out there, but…
I’m going to stop now as I think that’s enough to have you ponder more deeply what you want/hope to… It could be that others will chime in to disagree with one or more things I’ve said above, and that’s fine, I’m eager to hear such myself (as I’m not some super master at all this who knows everything).