I am looking to learn about the philosophy of Tibetan Buddhism. Does anyone know the proper order in which to learn the texts?

I dont know what your reasons for study are or much about the BP but I would say to study Lam Rim extensively. This is because it is the key to all sutra - this is why it is important. Tsongkapas is best because it is so extensive. It includes a really useful presentation of the Consequences school but not how to meditate on it. So for this turn to Meditation on Emptiness by Jeffrey Hopkins which includes the Gelug presentation of phenomena. This may (may) be useful to cut through a lot of the other schools messiness with regard to their presentation of phenomena and psychology.

Im not being partisan. But there is a problem, as it seems to me, an outsider not concerned with legacy, that a lot of the schools other than Gelug evolved without Consequences school view and thus with hang ups regarding abhidharma and psychology and logic generally. Dont get me wrong, it is precisely for this reason the Gelugs themselves are very riven and withdrawn. Cut to Prasangika. This course of action does not contradict the Buddhas teaching, nor devotion to any teacher or practice of any lineage as there is only one root to cut!

The trick would be to use this clearer (quicker) knowledge of the Gelugs to engage with the method side at the highest level in the your practice, your creative method, how you choose to engage with the lineage you feel most attracted to, to practice guru yoga with a teacher (real or imagined) as the unity of the two truths. The Gelugs have this too (see Sonam Thakchoe on the two truths) but in practice its a whole other ball game (see His Holiness the Dalai Lama on the Gelug/Kagyu tradition of Mahamudra).

The study material of the 'basic-program' provided by the FPMT covers a great deal, but (1) what it covers also depends on the teachings and commentaries you follow (2) and it is a specific traditions and a specific college. You will learn there are various traditions, and various college that propound different point of views. Once you are familiar with one and firm you will understand the other better as well. You can read the study material - root-text, recommended books, transcripts of past BP - but you would not get that much out of it. You would definitely get more by attending a BP, either online or residential. I advise you not to just study on your own. Receiving teachings from a qualified teacher is of utmost importance.

The BP is done in 2 years in some centers, 3 in others, 5 yet in others. Because of this, the transcript of the course given by Geshe Chonyi on buddha nature (with Maitreya's root-text) is relatively short and easy and he quotes Gyaltsab Je's complicated commentary once or twice. Geshe Gyaltsen's transcript, on the other hand, is long and it is a word-by-word Gyaltsabe Je's "oral" commentary that he gave over three months. I know because I attended as interpreter from English to French.

Some study Gyaltsab Je's commentaries while others do not (precisely because it's terse, dry, and not intended for beginners).

The BP is great. You would learn about Lam Rim (mainly Tsongkhapa's), Tenets (doctrinal classifications), Lorig (epistemology), Buddha nature according to the meaning of the Prajnaparamita but also the third turning, etc. It might have sectarian aspects but these are not avoidable. This is because the FPMT is spiritual, or "religious", although it is academic, it is not oriented towards inter-textuality too much, or historical perspectives. Comparisons (as are done in the context of Tenets) always have an agenda. Still, if you are a practitioner, at some point you will have to dive in a water that you will have come to see as - if not the absolute truth - beneficial, wholesome and functional and aimed to your goal, enlightenment.