Nice meeting you is used more when saying goodbye than when greeting someone...well I would say nice meeting you when I'm leaving than when I'm arriving because I know the person better than when I first met them...if that makes sense?!
Nice to meet you and glad to meet you would therefore apply when greeting someone or rather when you're introduced to someone.
As for glad meeting you, I wouldn't really use that at all
(I am) glad to meet you is correct.
(I am) glad meeting you is incorrect, and is not equivalent to the abbreviated form (It is) nice meeting you. One cannot say It is glad meeting you, as it has to be a person who is glad.
Once upon a time, you would have heard people say "Glad to meet you" when they were introduced, but never "Glad meeting you".
Once you've known someone a while, you might say "I'm so glad I met you...", but I don't think it's used so commonly now on meeting someone for the first time.
If you expand the sayings: "Nice meeting you" means "It was nice meeting you", but "Glad meeting you" would mean "I was glad meeting you", which is a structure that doesn't work. One is glad to be, or do, something, never glad being or doing.