Be clear on setting your goals
This is more like meta-advice for learning itself, but it helps. What exactly motivates the inquiry onto the language: is it to read Dostoievski in its original form? Or just to be able to navigate the simple, quotidian interactions in a foreign setting? Making that clear helps in choosing the most appropriate strategy. Theoretically, if a goal is just to read — and not to be conversationally fluent — I suppose it would be possible to, say, learn Greek without speaking Greek.
Audio materials for listening and speaking
My experience with Language Transfer has shown me the importance of listening and speaking from the very beginning. I would then, first, check whether they have done a course on a given language; otherwise, the closest would be Pimsleur (whose audio courses I am currently doing, for Danish, but it's not as holistic and interesting as LT), or Michel Thomas' method (which I never tried).
It also helps that this sort of learning can be engaged in outside of a desk environment — consider it for commuting, or for a walk in the park (there are studies on low-intensity cardio's impact on cognition — keep that in mind!).
The role of memorisation
The author of Language Transfer is particularly keen on ensuring students are not writing during the lessons. I think this makes sense, but why not make use of Anki and the spaced-repetition techniques for optimal, reliable memorisation of material?
Not using Anki in the context of language learning (unless it really doesn't work for you — in which case, huh, that's a very interesting cognitive situation?) is like choosing to walk over riding a bicycle: albeit it might be equally pleasant, and it surely is not a wrong choice...one could be faster and more efficient.
I don't think it is possible, or advisable, to memorise grammar — but even there one can arguably find methods for SRS to assist in the process. Vocabulary, on the other hand, can be effortlessly recalled after just a few days of practice.
Not only speaking and listening: reading and writing, too!
Here's another point where I would disagree with the LT approach: writing is fundamental to how I approach a language, although, granted, it can come a little later than basic listening, speaking, and grammar comprehension.
Writing may highlight, via orthography, subtle differences in the language, and it expands the modes of expression: we don't write and talk the same. As for reading, especially when tackling material that matches one's skill in a language, provides immense benefits in acquision of vocabulary and unconcious strengthening of grammar practices. !!! Aim for immersion from the very beginning
Immersion doesn't mean one is expected to understand everything immediately — that would be impossible — but exposure (not to the point of distress, of course) can only help. And there's so many opportunities nowadays: partake language exchange Discord servers or platforms; watch TV shows with either subtitles or audio on target language (or both!); listen to music, or radio shows; read the newspaper, or children's books.
Ensure exposure to both formal and informal discourse, and make good use of the internet!