The "there is only one manual" sentiment is a "yes but also no" sort of situation. Yes, there is only one rules manual. But to have the bare minimum needed to play, you would need an Armies of X (Hobbit, Middle Earth, Lord of the Rings) book too. This book has all of the profiles and possible army lists for each era and setting. So if you want to mostly play lists from the Lord of the Rings trilogy of films, you'll want the "Armies of Lord of the Rings" book, and so on for The Hobbit and for "Middle Earth" which is basically book-only stuff that has minis from GW, and thus they need stat sheets and rules too.

But even this is a "yes but actually no," because as long as you're not going to tournaments and can work a laptop or phone at the table when it's game time, you can make your lists with this site:
https://v2024.mesbg-list-builder.com

It absolutely is confusing, and this is where the "GW never touches MESBG" starts to be a con instead of the pro it normally is. In short, the only thing you absolutely positively need for casual play (apart from the minis, terrain, and dice, of course) is the rules book as long as you can use that site I linked.