The Rambam did hold his book the Mishna Torah is sufficient to know the Oral Torah, however look in the "Laws of Talmud Torah" where he explains that one divides his day into three parts, and one is for deepening one's understanding of the Oral Law, and also the subjects that he briefly touched on in the beginning of Mishne Torah which are called ''Pardes'' and are in fact the areas of Physics and Metaphysics.[He goes into more detail in the Guide.]
If one has a authentic Litvak yeshiva in his area, he should definitely go there to learn Torah,-- especially with a learning partner. But if not, the best thing is to make one's own space into a place of Torah.
I also am a big fan of speed reading in Torah. That is-- to say the words and to go on. That is to have a session in Gemara, Rashi Tosphot in such a way that he will eventually finish the whole Oral Law i.e. the two Talmuds, Tosephta, Sifra, Sifri, and the Midrashim. What one does not understand here, they will remind him of in the next world. I am also a big fan of Rav Shach and Reb Israel Salanter, and thus I believe that everyone should go through the entire Avi Ezri of Rav Shach at least once, and all the books of the disciples of Reb Israel Salanter on Torah Ethics (plus the books of Musar of Rav Yaakov Abuchatzeira the grandfather of Bava Sali).
[To understand the Rambam I also think it is important to learn the books and letters of his son, Reb Avraham, and of course the very important Guide for the Perplexed. Some people are so perplexed they do not even know they need the Guide. Reb Avraham Abulafia wrote that the secret of the final redemption is contained in the first forty chapters of the Guide.
In case it is not clear what I was saying: The Mishne Torah is good as an introduction to Torah, but it is a terrible idea to decide any halacha without knowledge of the Gemara and the source of the halacha as the Mahrasha and Maharshal wrote and many others.
[As for learning Halacha as they do in Authentic Litvak Yeshivas for 45 minutes in the morning my basic feeling is to get through the entire Tur, Beit Yoseph, and Bach. I consider that the prime Halacha book. Though I admit the Aruch HaShulchan is a close second.] [For the halacha session in the morning I recommend one of three things: (3) Rambam Keseph Mishna, (2) Tur, Beit Yoseph (3) Shulchan Aruch with the Beer Hetev.
You can bring support to this idea of the Rambam from the LM Vol II. chapter 12 of Reb Nachman. This idea is this :Even though God's glory fills the whole world there are areas where his glory does not reach. מקומות המטונפים as it says in a verse וכבודי לאחר לא אתן. But since nothing can exist without God's making it exist every second how can those places exist? Answer: They get there life force from the מאמר הסתום. That is in Genesis it says for each act of creation He said" The tenth statement is the very first statement In the beginning God created heaven and earth. That is the highest statement corresponding to the sephirah of Keter the crown. So when one turn to God from those places where God's glory is not apparent he gets sustenance from the highest level of the Crown and brings up all the fallen souls.
There are many other places in the LM where you could bring support to the Rambam like what Reb Nachman says about stories. This is to be expected because the thought of the Rambam and Reb Nachman are in general highly correlated.