Courtship isn't dating. It's only begun when one is ready to settle down and get married. You've got the rest of high school and college ahead of you. It's not unheard of for chaste couples to marry while in college but it can be more difficult in some ways.
I would draw the line at holding hands. I wish for my sons to save their first kiss for their future wife. Many consider that to be unrealistic, I do not.
Timeline for courting is entirely up to the couple, but I would say a calendar year, including all the holidays, so as to get to know each other's family traditions, etc.
Courtship usually involves the families of the couples, including siblings, instead of one on one dating. That way, there are more people around to help stop any temptations to be less than chaste. It is the way things used to be, before "dating" became common.