Which books to buy to start playing Warhammer 40K 8th edition?
Strictly speaking the barest minimum needed to play would be Index: Imperium 1 and Index: Chaos. If you already have the CSM Codex you can do w/out Index: Chaos. You do not actually need the Codex: SM for Blood Angels. They will eventually get their own codex, but in the meantime you could either use the Index or the Codex until the chapter specific book is released.

You do not need to purchase the rule book, but you'll probably want to. The core rules (about a dozen pages) are available for free. However the main rulebook does have a lot more options for play, more missions, and advanced rules, plus fluff and more.