here is another cheap way to get started that involves just a little research to get started type in the words "raku instructions" on Google. Raku is a Japanese pottery style that requires much less heat than kiln firing.
It must be noted that Raku Is Definitely no food safe... but a great start for art pieces.
Raku is usually bisque fired and when glazes are applied, they go to cone 05-06 which I believe is around 1200F.
I know you can do pit firing or wood firing which doesn't involve a kiln and there are a few good books on alternative firing techniques.
If you are struggling to get pieces glazed/fired within a class time, find out if there is open studio time that you can go in for glazing pieces. If your class ends and you have limited time to glaze/fire... sometimes talking to the place that hosts the classes will allow pieces to go in after the class for firing. I know my instructor will allow former students to come in for a class to fire (esp since it is raku and you have to be right there for the firing).
As for the glazes not being marked.... that's a huge problem! If they are a larger "school" offering classes, you might want to bring this up to the instructor as well as working your way up the food chain (director, board) simply so that this issue can be addressed, even if its just a sheet that needs to be pointed out at the beginning of the classes.