Pāramitāyāna and Tantrayāna

The answers above are great, but I want to address two sub-questions specifically.

1. Is this a good high-level view of (introduction to, or taxonomy of) Tibetan Buddhism?

It is important to note that Tibetan Buddhism is not mutually inclusive with the Mahayana. That is, "Tibetan Buddhism" are just those forms of Buddhism which trace their lineage from the Sanskrit tradition of Buddhism in India as opposed to the Pali.

Within Tibetan Buddhism you can find fully formed paths other than the Mahayana (Bodhisattvas vehicle) including the Hearers vehicle and the Solitary Realizers vehicle.

2. To what extent is it true that "practitioners have the choice"? On what basis should or do they choose (e.g. which practice path is suited for, or available to, what practitioners)?

Teachers or lamas in Tibetan Buddhism are supposed to teach students according to their capacity. Of course, unless the teacher is a highly realized being it might not be possible to correctly measure a students capacity in all cases. That said, it is my understanding that teachers should strive to do this to the best of their ability.

For instance, it is considered a very grave transgression to teach emptiness to dharma students who are not ready for this teaching. Why? Because it can be harmful to themselves and others by causing the student to misunderstand emptiness and believe that it doesn't matter whether we conduct ourselves virtuously or not... etc.

Now, it is also best if students take some responsibility and do some self-diagnosis to decide what they are capable of in the same way students are encouraged to really check for themselves about the qualities of the teacher.

I hope this helps to prevent misunderstandings and encourage beneficial dharma practice. For more, I highly recommend reading Buddhism: One Teacher, Many Traditions.

The quote is more or less true. The position that Tibetan Buddhism distinguishes between pāramitāyāna and tantrayāna is accurate. Pāramitāyāna is most often translated 'perfection vehicle' or 'sutra vehicle' while tantrayāna is usually translated as 'tantra vehicle' or 'secret mantra vehicle'.

In the Middle Length Lam-Rim, Tsongkhapa says:

[Atisha] held numerous lineages of masters such as the two lineages of the common vehicle and of the great vehicle, with regard to which there are the two – (1) the perfection and (2) secret mantra [vehicles]. In the perfection vehicle he held three lineages: the lineages of the view and of conduct, the latter of which has the lineage from Maitreya and the lineage from Manjugosha. In the secret mantra he had received five types of transmission as well as numerous lineages such as the lineage of teaching systems,[tenets] the lineage of blessings, and the lineage of various instructions.

In this context, 'common vehicle' refer to:

a lineage common to the Hinayana and Mahayana

As Geshe Jampa Gyatso phrases it in his commentary to Tsonkghapa's Middle-Length Lam Rim. These refer to the teachings and practices 'common to beings of small capacity' (wishing for a precious human rebirth) as well as those 'common to beings of middling capacity' (wishing for abiding-nirvana, individual liberation). One might say that, of these two, only the linage common to beings of middling capacity is a fully qualified path, because a path is found in the continuum of a practitioner generating effortless, renounciation, that is 'a mind of definite emergence from samsara'.

'Great vehicle' refers to the practices exclusive to 'beings of great capacities' (those wishing for perfect buddhahood, that is non-abiding nirvana, freedom from both afflictive and knowledge-obscurations). The entrance to the Mahayana path is effortless renounciation + uncontrived bodhicitta (whether it be aspirational or engaged).

Within this category of teachings [of the great vehicle] you have indeed the two 'vehicles' or 'lineages':

1. Perfection vehicle
2. Secret mantra vehicle

As Geshe Jampa Gyatso writes:

The lineage of the Mahayana has two: (1) the perfection vehicle and (2) the vajra vehicle. In the perfection vehicle there is also two: (1) the lineage of the view and (2) the lineage of the conduct or the lineage of the vast. One lineage was passed on from Buddha Shakyamuni to Maitreya, to Asanga, to Vasubandhu, to Arya Vimuktisena, and so forth. The other was passed from Buddha Shakyamuni to Manjushri and so forth. In the secret mantra lineage there are five lineages. There is also the lineage of tenets, the lineage of blessings, and the lineage of instructions. As both 'vehicles' are Mahayana, they serve the same purpose: causing one to achieve enlightenment in order [for him] to benefit all sentient beings. Prasangika-Madhyamika claim that one has to come to practice tantrayana/secret mantra vehicle to achieve full enlightenment (and could not get pass the tenth bhumi without it). This is merely because the secret mantra vehicle purifies one's mind all the way through.

The perfection vehicle includes what we call 'the linage of the view and that of the conduct' or 'the profound and the vast' or 'wisdom and method' or 'the view of dependent-arising and great compassion'. It is so significant that, as Geluk students, teachers often say to us "if anyone asks you what Buddhism is all about, answer that it is about the view and the conduct: the meaning of dependent arising on one side, great compassion on the other".

Furthermore, we claim that a path is entered upon generating definite emergence. That a path of the perfection vehicle is entered upon generating bohdicitta as well (because it is a Mahayana path), and that the tantra path is entered upon generating renounciation + bodhicitta (becaus it is a Mahayana path) + realization of emptiness (whether it be inferential or direct, although this is a subject of debate). It does not mean you can not engage in tantric practices such as, say, Medicine Buddha Puja, or Guru Yoga, and so forth before having realized emptiness. On the contrary, we claim that engaging in those will get you plant the seeds you need to come to be able to actually practice tantra. You can not practice it unless you had a transmission or at least a permission from a qualified teacher, though.

There are four degrees of Tantra, but I will not go into that. This being said, Tantra has to do with understanding that one's aggregates are created by karma, it is playing with 'pure view' and the notion the behind the veil of the two obscurations, phenomena are naturally pure (as in 'abiding in natural nirvana'), and it encourages us to 'take the result as the path' as the Sayka emphasize very much (they call it Lam-Ré). This 'taking the result as the path' can take the aspect of self-generation visualizations (you generate yourself in the aspect of this or that deity manifesting from emptiness).

There are differences in tenets between tantra and sutras as well. The notion of 'subtle wind that goes from one life to the next' is hardly a notion of the perfection vehicle.