In the student phase of life (Brahmacharya Asrama), the student has to take permission from the Guru before beginning the recital. Before that he must also sip some water, as prescribed, to get purification.
He also has to clasp the Guru's feet in order to show respect before the recital begins. So, in situations, where the Guru isn't physically present at the spot, saying "Sri Gurubhyo Namaha" is a correct thing to do.
Usually in all Hindu traditions, appeasing Lord Ganesha is also done (at the beginning) so chanting Mantras for him at the start is all right too.
Manu Smriti 2.70. But (a student) who is about to begin the Study (of
the Veda), shall receive instruction, after he has sipped water in
accordance with the Institutes (of the sacred law), has made the
Brahmangali, (has put on) a clean dress, and has brought his organs
under due control.
2.71. At the beginning and at the end of (a lesson in the) Veda he must always clasp both the feet of his teacher, (and) he must study,
joining his hands; that is called the Brahmangali (joining the palms
for the sake of the Veda)
Since this recital is happening under the supervision of the Guru, the Guru asks the student when to start/stop.
2.73. But to him who is about to begin studying, the teacher always unwearied, must say: Ho, recite! He shall leave off (when the teacher
says): Let a stoppage take place!
Another fundamental rule is one should begin any Vedic recital only after pronouncing OM. And, one should do the same after one has finished the recital too.
2.74. Let him always pronounce the syllable Om at the beginning and at the end of (a lesson in) the Veda; (for) unless the syllable Om
precede (the lesson) will slip away (from him), and unless it follow
it will fade away.
Also, regarding whether one should begin the recital by saying something like Harihi Om, then that is not mandatory. But reciting OM is.
And, here is a related question on that: Do all Vedic mantras start with "hari om"?