Quick answer
Mucho gusto.
the everyday version
Encantado. / Encantada.
the alternative — see below for when
Which one to use
Mucho gusto is fixed: everyone says it the same way, whatever their gender. That makes it the safe default.
Encantado is an adjective describing the speaker, so a man says encantado and a woman says encantada — it follows the person talking, not the person being greeted. The full form is encantado de conocerte, or de conocerle in formal situations. On leaving a first meeting, the past tense is used: un placer or encantado de conocerte both work.
All the versions
Where you are matters
<b>Mucho gusto</b> dominates in Latin America, especially Mexico and Colombia; <b>encantado</b> and <b>encantada</b> are heard more in Spain.
Check yourself
A woman introduces herself. Which form does she use?