Empieza is the right way to say it
If a verb has both a regular and an irregular form, you can pick whichever one sounds better to you or conveys the voice you desire.
- Los padres están conociendo Oaxaca.
- Los hijos están esquiando en Utah.
- El abuelo está pescando en el océano Pacífico.
- La abuela está comprando arte en una galería de Coyoacán.
- Los primos están haciendo turismo de aventura.
- El tío está montando a caballo en su rancho.
- Los sobrinos están disfrutando de las vacaciones.

In this case, the present progressive is being used, the verbal periphrasis is composed of:
- <em>Subject + "estar" (conjugated) + verb (gerund) + complement</em><em> </em>
The <u>present progressive</u> is used to express actions that are in progress right now.
Sophie.- Hey Charlie, some are the same and others are different here in Charlie.- Yes. Here is to arrive 15 minutes to the appointment to arrive. Sophie.- But in the United States, it's time to arrive at the right time instead of arriving. Charlie.- Other manners are the same as ours at home. Sophie.- Yes, like the elbows on the table. It is used at home as well as in Venezuela. Charlie.- So, if I have manners at home, I will not have problems at the home of Professor Zambrano. Sophie: Of course not, Charlie!