Different teachers will prefer different methods. Some of it also depends upon your view of Jhāna. Personally I view Jhāna as absorption, without the 5 senses, and prefer the method of being mindful at the tip of the nose. I was reading a translation of the Dharmatrāta-dhyāna-sūtra a while back, which comes from the tradition of the Dārṣṭāntika. It was interesting to find that they too recommended placing one’s mindfulness at the tip of the nose, in agreement with their southern counterparts in Sri Lanka.
Discourse on Higher Advancement (parākramaṇa-bhāgīya) in the Preparatory Path (prayoga-mārga)
5.1 Bhikṣus practising Ānāpānasmṛti will proceed to higher distinction (parākramaṇa-bhāgīya) in their spiritual cultivation if they have successfully abided in positive effects. Their prajñā will also be enhanced. I shall herewith expound it in orderly sequence.
5.2 Once having advanced after abiding in positive effects, the practitioner should, again, abide in positive effect. That is why it is essential for any practitioner to abide in positive effects for the sake of attaining higher distinction (parākramaṇa-bhāgīya) in his practice.
5.3 Meanwhile, he should always concentrate on his nose-tip, making his mind bind firmly there, focusing all his thoughts in the proper observation of the wind. He should then keep his in-breaths and out-breaths firmly in mind and follow them closely in his recollection (anusmaraṇa).
5.4 If he does that well without laxity, he has initially abided in positive effects. Once this has been achieved, then he should keep up his preparatory effort (prayoga-mārga) for further advancement.
5.5 Then the practitioner‘s quest for further benefit will bring about positive abiding, followed by higher distinction (parākramaṇa-bhāgīya). Furthermore, it should also be noted that higher distinction will simultaneously bring in the abiding in further positive effects. Hence, when one passes the positive abiding state and advances further, another abiding in positive effects will come forth.
5.6 Therefore, once the practitioner appreciates fully well the various patterns of ānāpāna (exhaling and inhaling) and their ensuing benefits (guṇa) and faults (doṣa),for instances, whether his breathing is light, or heavy, or cold, or warm, or delicate, or rough, or sticky and or smooth he will fully understand that the concentration on ānā (exhaling) which combines with that of apāna (inhaling), can maintain control over his faculties (indriya-s), with their cognitive objects (ālambana) quietened and subdued to tranquility (śamatha) and nirvāṇa.
5.7 Similarly, there is also a similar way to control the wandering thought-concomitants (caitta) by counting the breaths and focusing on how they enter the body. This, is the essence of ānāpāna (exhaling and inhaling) which stops one‘s thought from chasing the cognitive objects (ālambana-s) Even one‘s thought of the cognitive objects will also be extinguished by its control.
You don’t have to place mindfulness at the tip of the nose though. Even the Visuddhimagga allows for simply being aware of the breath instead. What is important, if practicing mindfulness of breathing, is to be be continuously aware of the breath somewhere and to calm the mind until it becomes tranquil, still and one-pointed. The Buddha mantras are usually a means to anchor your attention to the breath, but sometimes can be used as a calming practice in their own right.