Hiya, Megara!
Ok so.
You do not have to buy a professor character, however you do have to be accepted as one, and spaces are limited. Applications are available under "Hogwarts Applications" in the forum "Professor Applications" and are opened between the 1st and 15th of the summer term (i.e. April, August, December). There will be a list of what classes are available and require professors, but only a few applications are accepted per term.
From starting, you are allowed 1 student character at Hogwarts. You may use Gringotts points to buy yourself "split focus" which will allow you a second. It costs 75o points. Check the
Gringotts Exchange for more information regarding earning and recording Gringotts points.
If you have any other questions, don't hesitate to ask!