Updated: Update: 2020.06.01
The form of the traditional greeting depends on whether you greet a male, female or group (skipping the less-frequent situation of greeting a group of females). Generally, the group form is used to include the family as well.
To a group (including a mixed-gender group): שָׁלוֹם עֲלֵיכֶם
To a male: שָׁלוֹם עָלֶיךָ
To a female: שָׁלוֹם עָלַיִךְ
Generally, the group form is used to include the family as well.
To a group (including a mixed-gender group): עֲלֵיכֶם שָׁלוֹם וּבְרָכָה
To a male: עָלֶיךָ שָׁלוֹם וּבְרָכָה
To a female: עָלַיִךְ שָׁלוֹם וּבְרָכָה