My favorite trifecta for basic grammar is Japanese the Manga Way , A Dictionary of Basic Japanese Grammar , and Making Sense of Japanese: What the Textbooks Don’t Tell You .
None of those books have any exercises so success with them assumes you’re good at developing your own practice curriculum to drill the concepts in. It worked fine for me but I’m old enough to have learned how to learn. If you prefer a more structured approach with extra guidance then replace Japanese the Manga Way with Genki I + II plus its workbooks.
I’m a bit sour on Genki, and have been for a while, so it’s always nice to see other resources I can suggest to beginners instead of just being like, “Well, you’ll have to unlearn some of this later, but it’s the best there is, so bite the bullet.”
Lack of accompanying practice/quiz material can be off-putting for a lot of learners, though. I know it is for me, personally, when I’m actively learning brand-new material rather than just listening/reading for exposure.
Are there any good practice/workbook-centered materials that have come out in the years since I completed Genki, or is that still unfortunately the best starter material out there if you want that?
Re: OP: No matter what you go with, make sure you’re getting structured grammar-learning in somewhere! Japanese shares virtually no structural logic with English, so you can’t get by on vocab alone.