Purely because WaniKani doesn’t teach vocabulary in the order of importance I’d say you can start immediately. The Tadoku graded readers (the ones I sent screenshots from) are pricey, but if you don’t have any previous experience learning Japanese I can imagine they’re well worth it.
As for grammar you’d need to know you can check out their site: にほんご よむよむ文庫 Japanese Graded Readers – レベルについて – アスク出版 日本語教材
Level 0 readers for example expect you to know the following grammar:
present form, past form, interrogative, ～たい, etc.
※ です and ます endings in the main.
For more resources or if you have more questions regarding graded readers in general you should check out this thread Graded Readers and Parallel Texts "Book Club"
I had already studied Japanese before I started WaniKani, so my advice might not be as helpful as that of some of the folks in the Graded Readers thread who started their Japanese journey with WaniKani. 
All the best!