Man says "encantado" but woman "encantada" /

these are correct ways but very formal. As you are young, sure you wouldnt use them too much when introduced to other youngers, specially in informal contexts. I cant give you the present time ones as i am out of fashion now. So, look for some young to tell. There are some formulas that may help introduce youself showing a bit of your expectations or your standpoint before the ones you are introduced, be a mate, a girl, for fun time, for etc. They are quite normal, nothing to do with slang or ingroup pertenence or alike. Just, habitude. (talking about younger people).

¡Mucho gusto! ¡Encantada/o!

Mucho gusto,..encantado(a)...

"Encantado de conocerte" or "Mucho gusto"