Preserve them by scanning them and sharing them.

I have a website dedicated to preserving old magazines.

http://www.vintagemags.net/

I have done faux finishing in the past and I would take the ones that I just loved (pictures) and glue them to the wall of a study or office like wallpaper. When you are done, the next day pop any bubbles with a straight pin then glaze with a little raw or burnt umber paint mixed into some waterbased sealcoat.  Thsi will make them look aged and also preserve them.  HAVE FUN!

Well if you really don't want to get rid of them then in my opinion they need to be stored in a way that is both usable and attractive.   Not to mention fairly easy to get to the ones you want when you want them.

Being an art teacher I'm sure you'd like them to be used in an artsy way too.  So what about magazine cubes that can be used not only to store your mags, but be useful as furniture?

 Alone they could be end tables or night stands. 

Three at the end of your bed with a long cushion could be a bench.  Or in front of your couch with a wood or glass top for a coffee table.

Two or three cubes could be stacked for pedistals for plants.

Four grouped in a square with a glass or wood top could a cocktail table or cushion an ottoman/cocktail table. 

The cubes could be made out of many different materials, but I think plexiglass framed in wood would be neat so you could see the mags through them.

Whatever you do make sure you inventory them adding special items in each issue to the list and what cube they are in so you can find them when you want them.  Oh and have fun!