If you are a 13 year old girl do you handshake or hug another 13 year old girl the first time you meet them?

Just say Hi.
I don't know any 13 year olds who do either with other kids, unless their grandmother is standing over them making them do it.

Neither. Physical contact for children that age is inappropriate and your question reeks of "pervert."

Neither. Usually you just say "Hi, I'm 《name》!" No touching involved.

Do nothing. Not a good idea to hug someone you don't know, and grls generally don't shake hands. Follow the other persons lead.

handshake

Tell her to just say "hi" to each new girl and introduce herself the first time she meets a new girl. A handshake is too formal, and a hug is too affectionate for someone you've just met.

I don’t know, the same as what your mother would do if she met another female her age.

Kiss each other

or a kiss

Probably handshake until you know them really well