Your question is a good one although in terms of site guidelines, it may get a recommendation for closure because the answer will be mostly opinion.
Resist the idea that you don't have enough time. Like with all types of Torah study, regular, fixed study, no matter how small or large, is the more important goal. Adding Navi to your seder should not diminish from whatever your current studies are.
In terms of order, follow what Chazal have set up for you, meaning the order as the books appear in Tanach. The oldest authoritative Tanachs which we have access to are the Leningrad Codex which was written in the 11th century CE and the Keter Aram Tzovah, also known as the Aleppo Codex which was written in the 10th century CE. Rambam, along with many others, acknowledged the accuracy of the Aleppo Codex. They both list the order of the later prophets as Isaiah, Jeremiah, Ezekiel, and the twelve minor prophets. This is also the order followed by Rabbi Don Yitzchok Abarbanel in his commentary to the later prophets.
There may be some question about this because the Tur in Yoreh Deah 283:5, and Shulchan Aruch 283:7 citing the beraita in Bava Bathra 14b place Isaiah after Jeremiah and Ezekiel. But Aruch HaShulchan 283:14 acknowledges that the order cited in Bava Bathra was not followed after their day. The order was set with Isaiah first.
It is possible that the order from Bava Bathra is only relevant when the Tanach is bound in a scroll, like a Sefer Torah. This would relate to the view of the Rema cited in Aruch HaShulchan 283:6.
But this doesn't answer the reasoning for the order found in these two early, authoritative sources from expert Soferim. To this one can look to the Tur, Yoreh Deah 275:11 which quotes Rambam saying there are many things that are required for sifrei kodesh which are not recorded in the Talmud but are the minhag of the Soferim passed down among them only orally.
It is suggested that the reasoning of the Soferim is based upon how the content of each of the later prophets is described in Bava Bathra, that Jeremiah is about the destruction of the Temple, Ezekiel is a mixture of the destruction and the salvation, while Isaiah, the prophet of the redemption, is about salvation only, the geulah.
The order used by the Aleppo and Leningrad Codexes, which is how most printed Tanachs are ordered, is based upon the teaching of Raba and Reish Lakish found in Megillah 13b. That G-d does not smite Israel before first creating the remedy. The remedy, the prophecy of salvation, comes first. And this principle also follows the teaching of Rashi to Esther 3:1 and parshat V'Etchanan 6:25 as well as Rabbi Chaim bar Avraham HaKohen of Aram Tzovah in his commentary Torat Chacham 311b on Esther 2:23 and the teaching of the Lubavitcher Rebbe in Torat Menachem Hitva'adiyut, vol. 47, pg. 244.
In terms of commentaries, Rashi, Targum and Radak are a solid foundation. If you have them, Arbarbanel and Malbim are worth including, but it is extra. Again, try to make it a fixed study with additions when you are so motivated and circumstances permit.
Try to keep in mind that the Navi'im chosen for the Tanach were selected from all those that were known because their prophecies applied to each and every generation. That means that there is a flexible/adaptive dimension to Navi in addition to the "correct" fixed intention.
Another very important thing to keep in mind is that the language of the Prophets is largely allegorical/allusion/hints. It is possible that some of the language can be taken litererally, but that is more the exception than the rule. And like with all Torah study, the primary idea for each individual is that it lead to action. המעשה הוא העיקר. So ones personal study of Navi is intended to refine and improve their performance of the mitzvot and their service to HaShem.