Learning the vocab first and then trying to read the lesson afterward is in fact the recommended strategy! At least, that’s what the beginning of the translation book recommends for proceeding through the text. This is what I’ve been doing, too, and it’s been working out really well for me. I take physical notes on the vocab and also start running them through Anki several days before I attempt to read the lesson. If you learn the vocab well enough (and read through the grammar section) before attempting to read the chapter, it minimizes a lot of the flipping back and forth that you have to do, and you basically end up being able to more or less read the Japanese text without needing to reference any outside aid as you’re reading, which is a cool feeling. The book seems to be structured pretty well where it slowly builds on grammar you’ve already learned and doesn’t add too much new grammar at a time.
My approach with Minna no Nihongo is to basically treat it like attempting immersion through resources like koohi.cafe (which is a website for pre-learning vocabulary before you read specific books and other materials in Japanese). I learn the vocab and read about the grammar points, then practice applying both of them by reading the textbook. I’m sure there’s plenty of stuff that I’ll get less practice on in the textbook, but I’m eventually going to read other books besides that one. MNN is just giving me a basic foundation that I can build off of.
I don’t really mind the book using the ます form, but I’m also reading it in conjunction with watching Japanese Ammo with Misa’s absolute beginners playlist, which has given me a basic understanding of how Japanese sentence structure and verbs and such work. I just view MNN as giving me more practice with the ます form. My Anki deck has the verbs in plain form as well as the ます form from the textbook so that I can learn to associate the meaning of the words with both forms (otherwise, I have a hard time recognizing WK verbs, for example, if I hear them spoken in ます form and not plain form, since we only learn the plain form here and never practice any other conjugation).
And @MrSuntastic, I’m not sure I’d recommend going through MNN after completing Genki. I feel like it would be a lot of wasted time, and also a waste of money, since MNN is fairly expensive. You’d probably be better off just picking up the grammar points you missed through reading manga or other native materials, or through other sources like A Dictionary of Basic Japanese Grammar, since MNN would contain a lot of stuff that’s redundant for you.
I think Genki and MNN are roughly equivalent, and either one will serve you just fine, so I would choose whichever one has a style that you prefer. Also, for the record, I’ve never taken a formal Japanese class, and I haven’t had any trouble getting through MNN without a teacher (other than Misa’s videos haha), because the lessons and exercises are structured pretty well for self-study.