I think the best response would be „nice to meet you too“.

You can say likewise

"Me too" only would be rude and person might get confused about what exactly you want to say...as while saying only me too a lot depends on your expressions and tone....rather I would go for 'nice to meet you too' simple n straight.....or "I feel the same" but it is kinda for whatsapp or text.

Informally you would say ‘and you’ which conveys and i am pleased to meet you also :)

Informally most people would say “You too!” Or “Nice to meet you too!”