Since this manga uses furigana readings on kanji, you don’t need to know any kanji to read it.
I’m not familiar with what grammar Minna no Nihongo covers, but chances are you’ll face two things if this is your first time reading manga in Japanese:
- You will encounter a lot of grammar you haven’t learned yet. You might even start learning more grammar at a faster pace than in your textbook learning.
- You might not recognize grammar that you’ve already learned from the textbook. This is because it takes time and repeated exposure for your brain to build up pattern recognition of grammar.
These points also apply more or less for vocabulary as well. You’ll encounter a lot of vocabulary you don’t know, and you’ll find you need to look up most words you encounter. (If you start reading with volume one, which we just completed, there are existing vocabulary lists that help out with this.) Over time, you’ll start to recognize common vocabulary, since it shows up often.
I recommend giving reading a try, understanding that the first material you read will be difficult no matter when you start, forcing yourself to push through one whole volume, and then decide if you want to keep going on manga reading, or take a break to learn more grammar (via textbook) and common vocabulary first.
What’s your experience with Takagi-san? Did you watch the anime with English subtitles? Read the comic translated into your native English? Have you attempted reading it in Japanese?