Minna no Nihongo is a beginners’ textbook, so jump right in. You’ll just have to be prepared not to know all the kanji or the vocabulary words, and I mean, that’s normal since you’re learning Japanese: the point of getting a textbook is to learn something new. Whether or not you want to try retaining the new kanji on your own is entirely up to you: I would do so by learning to write them, but I know that many people on WK don’t study kanji writing. You’ll probably come across them on WK at some point anyway, so studying them on your own might not be what you want to do. What I think you could try as a compromise is to get yourself a handwriting input option and to use that to look up new kanji to see if they’re on WK (just google ‘[kanji] wanikani’ and see if the kanji page comes up). You can then read through the page and see how WK tackles it. Take it as a lesson preview if you like.
I’d just like to say that even if you know all the kanji used in a given text, you might not know all their combinations, so there isn’t much of a point – in my opinion – in waiting until WK has given you ‘everything’ there is to know about the kanji in Minna no Nihongo, simply because it might not. That aside, you’re fairly likely to encounter some of the kanji you’ve already learnt on WK, which will only strengthen your memory and understanding of them. Whatever the case, all the grammar you’ll learn in a beginners’ textbook will allow you to start applying the knowledge you’ve gained on WK in reading and possibly in making your own sentences, and there can be quite a bit to get used to initially because Japanese sentence structure is so different from English sentence structure, so I think the benefits of starting early far outweigh the discomfort caused by any struggle you might have with the kanji and vocabulary used.
Hopefully someone with experience replies you soon, but from what I’ve heard (since I’m not a Bunpro user myself), it sounds like it really depends on which courses/modules you decide to do on Bunpro. I don’t think there’s a fixed curriculum. Instead, you choose the grammar points you want to study (e.g. JLPT N5 grammar, N3 grammar, N2 grammar). After that, you start clearing grammar points. I don’t know if there’s a level system, actually… it could even simply be that you go at your own pace unlocking one grammar point at a time? Whatever it is, while I could be wrong, I’ve never had the impression that Bunpro imposes a set workload on users by level, unlike WK.
EDIT: Yeah, from the Bunpro FAQ, it really sounds like you choose the grammar points you want to study.