Actually what it sounds like your looking for is what's technically refered to as a 2nd person game, which are far more rare than 3rd or 1st person games. Basically the difference between a 1st and a 2nd person game is that there is no avatar, or persona that the player assumes. You play as yourself. In terms of writing a story, this means that each student can say "I" did this or that, rather than "Gordon Freeman" did this or that. It can be argued that games like Battlefield 2, or even Counter-strike could be considered 2nd person adventures, but generally i'd say that it's important that a 2nd person game give no special abilities or training or in anyway enhance the actual persons real life skills. In counter strike i can get headshots from a distance, yet in real life my aim sucks. I don't have the foggiest clue as how to repair a battle tank or revive the dead, yet in BF2 i can do both of these things... In a second person game it's imporant that it neither provide or require any skills that the player doesn't already posses.
Echo: The lost Cavern is probably the most recent Myst clone. I haven't played it but reviews ranged from 65% to 90% on game rankings. It's rated E for everyone (at least untill someone makes a nude patch for it.
) and it's about 20 bucks so it's cheap.
Realms of Illusion is another option. I couldn't find a review but my gut says mediocre.
-- That's about all i could find that were in the E catagory and wouldn't require major gaming rigs to play. ( i assume your school's PC's aren't standard issued 128MB video cards.) and that were played from the 2nd person point of view.
Assuming your hardware can run it i'd stick with the various Myst games at the moment.