There is no universal correct pronunciation. Depends on where you from on and your preferences.
I would say
/ɑ/ as in car:
Aaron (don't like it pronounced like
Erin)
CaraKaraSarah and
Clara if outside English-speaking countries
TaraAriana
/æ/ as in cat:
CarolynMaryDarrenKaren
/ɛər/ as in air:
Sarah and
Clara (in English)
CaryGaryBarry
