Wow, 14 is quite a number ^ I'm sure you'll enjoy Madrid, it's a great city!
For some cheap tapas check out "El Tigre" it's a place that's always packed, you have to stand and fight your way through but you get loads of greasy tapas just by ordering some beers (cañas), it's a students favourite. Or go for the take away "lunch deal" (just a bocadillo with a fruit and sth. to drink) @ the Museo del Jamon and sit down in the Plaza Mayor eg.
Also make sure you get some "churros con chocolate" @ San Ginés, preferably after clubbing, it's always packed in the morning hours on the weekends ( http://www.notesfrommadrid.com/2007/...ria-san-gines/ )
Or if you'd like to eat out a little more nice, but still relatively cheap check out these restaurants: Finca de Susana, Bazaar, Ginger, La Gloria de Montera - they all offer great lunch deals (must be sth. around 10€) but are also good and cheap for a dinner - dinner starts at 8:30pm, no reservations and be prepared to queue (I guess it would be impossible to go with 14 ppl at once)

Have fun! :-)