To answer the question you specifically asked, “Going through Tae Kim” could look like this:
Do one chapter a week. Each week on day 1 read the chapter through and read the example sentences (this will take 10- 20 min). On day two put the example sentences into an SRS system with the sentences on the front and the english gloss on the back.
on day 4 or whatever re-read a chapter you read before. Do the SRS reps everyday.
This would take you about 20-30 min a day (with more the day you entered the sentences).
…Or some modification of this to more suit your personal preference.
To the point that others have made (or implied), this is not going to be enough. The nice thing about a textbook is it doen’t just go one way (can to read a sentence and “understand” it). A textbook asks you to do specific tasks (read the following passage and write the answers to the following questions, look at these clocks and write what time they say in Japanese, write a sentence that describes the action taking place in the picture, etc.) This kind of stuff while maybe boring, a - forces you to do something that can then be checked for correctness, b - can use and incorpoarate not just one grammar point but multiple points, vocab, cultural information, etc. And well written textbooks (like Genki or any of the others mentioned here) do exactly that. They slowly incorporate more language information into the tasks they ask you to perform.
But as has been discussed in this forum many times, Japanese grammar is not trivial (it is not super hard, but it is not “like” english or french). You will probably have to encounter a particular grammar point or construction many times in many different contexts and have it explained multiple different ways before you feel like you really understand it.
If you are looking for a system, I could suggest:
- Start with Genki and work out a pace that works for you (a chapter a week, every couple days, whatever)
- After you have done a couple chapters of Genki (or at the same time if you want) start going through Tae Kim in the sense discussed above
- when you start reading native materials (WK recommends at about level 10) you can then start using a reference (DIctionary of Baasic /intermediate Japanese grammar) to look up things you don’t understand.
- whenever in the course of doing the above things you have a question that isn’t answered by the resource you are using or you just want more information and examples on a particular topic, use one of the many online resources to get an alternative explanation or more information
If you do something like the above, you will pretty quickly find out what you feel like works for you and what sorts of online resources resonate with you etc. From there you will be able to find your own path.