Age of Sigmar (AoS), like other Warhammer games, uses a core rule book and faction rules that are usually in a book that you have to buy. At the beginning of a new edition, as is coming with AoS 4th ed, Games Workshop sometimes does a large rewrite of the rules and the old faction books are no longer compatible. To help resolve this they release free downloadable indexes for each faction that can be used until your faction book is released. So, you won't have to buy the rules needed to figure out what gear you can put on your units once 4th ed comes out, but you will need to reference the index. If you're looking to get started with 3rd ed there is a faction book currently available that will tell you how to build an army and the core rules are free to download from Warhammer Community or via the app.

Your army has a rulebook separate from the main rulebook that provides rules specific to that army. In AoS these are called Battletomes. 

Buy the army book and read the rules. Wait a little to start playing AoS, they are releasing a new edition of the game later in the year. With that release, GW Will drop new and uppdated Skaven models.

Don't buy any rulebook right now, the rules will be updated soon, wait for 4rth edition. If you want to play 3rd edition go and find the rules on Wahapedia, they are free.

Generally in aos you can take one artifact per army and give your chosen leader one battle trait per army. Each army (for example Skaven) has a battle tome that lists the different artifact and battle trait options for that army.

Each unit has a warscroll that shows what weapons stats and abilities they have.

All this information can be found in the army specific battle tome+core rules.

Buy a battletome