please think well of me, please take care of me (a newstarter after an introduction) / please take care (of) (when entrusting a person or piece of property to someone)

pleased to meet you / best regards / thanks in advance / thanks for your continued support

(polite, formal) well, acceptably

petition (the honorific form of 願い)

used as the word for please, familiar honorific.

Please (emphasize a request).

宜しく: (polite, formal) well, acceptably

(humble, formal, polite) Please (do). Humble form of お願いします (onegai shimasu).