The deposit should be made within a very brief time period. Extending this period too long will only make it more difficult to finalize your plans for travel. Two weeks should be plenty of time. All payments should be made directly to the travel agent if you are using one, or they should be made out to your institution. You do not want cash or checks going through you directly.
Payment is easiest in check or money order form.
You should keep a list of those who have paid and the date they paid. Also, you should make a copy of the check submitted and keep for your files and the schools files in case a problem arises. An account set up at your school's administrative, finance, or payment office will take you somewhat out of the loop. Also, if payments are make directly to the travel agent by the students or the parent, this will be easier for you too. This will keep you from having an onslaught of questions as you near your departure date.