I have compiled about a hundred books to read before I start writing a book I have planned, and feel I'll never write the book if I take the two or so years to read all the books first. Should I skip the research entirely and just write the book?
As I understand it, you have a story you want to tell in the fantasy genre, and that this would be your 'first serious attempt' to write a substantial work of this kind.
Whatever you do will be the result of a decision you make. Just make sure that decision is made for the right reasons.
To avoid research being an avoidance tactic, I recommend you put your story at the heart of the decision-making process.
Get to know your characters very well - inhabit the world(s) in which they exist in your imagination - find out how they speak, act, think. Work out how they behave in different situations, what their key personality traits are, and what changes they undergo in terms of character development, and why.
No book you read can tell you any of this. What other fantasy books will show you is how other writers have approached the same challenges for their characters in their stories. How-to books will give you frameworks and tools you can apply when you come to tell your story.
Let your story guide your research questions and try to relate your research to very specific research questions. 'What are three key effects on a planet of having two moons orbit it?' for instance. If there are no key effects that are instrumental on how life unfolds on that planet, do you really need two moons?
From there, it is a question of seeking inspiration and ideas in everything around you - and seeking answers to questions that arise as a result of you engaging with the process of writing the story.
I personally find it useful to map the story structure first - I do this by outlining the events in each character's story line in chronological order, noting where they intersect and how conflicts are resolved (or not). I then plan the structure of the book (the reader's journey) and then write.
My writing process often isn't linear - I may write the ending, descriptive elements, and some key scenes before working on passages with dialogue. Others will take a more linear approach.
The only right way is the way that is right for you. Find a way that enables you to get your work finished, edited, beta read, potentially pitched, and eventually published.
You should prioritize writing.
If you're making a list of books to read before you start writing, then what you need is not simply read the books, but to go to school for these books/subjects. That way you can truly focus on the subject at hand. Professors can point you things you otherwise wouldn't have known about, plus you and your colleagues can discuss these things over drinks, which expands and reinforces the research.
If this is not an option, know that very many novels and stories did not turn out the way they were though of/not planned; They only had an initial idea and everything else grew around them. The idea behind The Hobbit for example, was a single line, that J.R.R. Tolkien wrote in his notebook: "In a hole under the ground there lived a hobbit.". "Lord of the Rings"'s central idea was a fictionalization of WWII.
Besides, the difficult part is not the research, but the writing itself. World building is simply the collecting of ideas. It's pulling the ideas together into something someone else would want to read, that's where the work lies. Of course, knowledge of things is useful, but it cannot be the central premise of what you're writing, if what you're writing is going to be interesting.
Remember also that no novel, or short story even is written in a single setting. Writing anything is like taking part in a marathon: slow and steady wins the race. Get started with writing, read the books while you're doing it and you will find where your gaps of knowledge are (which guides your reading) and you will likely find that writing is the actual challenge of your project.
Here's how I do it:
I use the Snowflake Method of Writing and whenever I get stuck, for instance describing a character's background or figuring out something on setting or a worldbuilding detail, I do research.
Then, of course, I can get sidetracked by research or think I need more than I really do, and start building a whole dynasty with a family tree 58 generations long... and maybe that could be staved off by doing more structured research... but I've never compiled a list of books to read before writing a novel.
I think, to me that would be a sign I'm setting myself up for failure... like someone told me to write the book in school or something and I didn't feel like it so I hit them over the head with a pile of books...
That being said, some authors do, indeed, read tons of books before writing. For instance, Herman Wouk did before writing the Winds of War and its sequel.
However, from your question I surmise, that even if you would end up being an author that does read books before writing, you need to figure out that you are and that you need to, first, so start writing or maybe write a synopsis and do the research as you need it.
Yes and then again no.
Getting ideas on paper is often the most important and challenging part of writing; don't let anything stop you from doing as much of it as possible.
You will find that research informs new ideas and alters the ideas you had when you started the work and that's not a bad thing. Absolutely do make sure to put in the effort to researching what you are writing about just don't let it slow you down when it comes to composing the story. You will also find that the story that you start writing will make some of your research redundant and prioritise other material which will make that mountain of books easier to tackle usefully.
I really love the answer provided by Leon Conrad. I would also like to add that it depends on the chosen genre. If you want to put some historical facts in your story then, of course, you need to do some research. You can skip the research for a fantasy novel. Thus, the golden mean is to pick the most important books for your story, explore them at least a little, and start writing.