Agreed the Grand Alliance books were mostly released when
AoS first got sensible rules and are quite out of date now.
The Big Rule Book gives you the alliance abilities, core rules, battleplans and also a nice chunk of meaty lore to read up on.
The Sylvaneth Battletome gives you all the lore and rules of the Sylvaneth along with their battalions (of which one, as said, features Stormcast). In addition it will give you all the options and lores to run that faction on its own as well. So you can vary between a full grand alliance force or Sylvaneth with stormcast allies.
Stormcast Battletome is the same, only it won't have a dedicated Sylvaneth battalion. Otherwise it gives you a good background and core for the Stormcast as well as all the warscrolls and such and, again, lets you run a stormcast force with Sylvaneth allies.
In addition you'll want to pick up the Generals Handbook 2018 for and updates it gives to either force (most likely on the syvaneth). The main difference is that battalions went up in points with 2.0, though you can get those details from the free warscroll builder on the Warhammer Website.
https://www.warhammer-community.com/warscroll-builder/
So that's two Battletomes and the Big Rule Book and the Generals Handbook 2018. In addition if you are doing
AoS now you'll likely want to pick up the Malign Sorcery boxed set, both for its book and the models for Endless spells. Note that the book in that doesn't contain many rules, but it does contain all the realm artifacts and lores and such that you might well need if you like/your area uses realm abilities. So that book is more of a "pick gear and note down its bonus on your army list" rather than one you need to consider consulting game to game (like the rules or stats for armies).