I might be putting my head on the chopping block... but I would recommend that you go to a liberal arts school and get a degree in anything, then move on to a stage management career after college. Take theatre classes and certainly learn everything you can while you have the chance to approach SMing academically. But having a well-rounded background is something I have come to value. I would give the same advice to someone planning to be an engineer who might want to enter a special tech program, or a senator's son who was determined to take only poli-sci classes at an ivy league school. Take advantage of your undergraduate years to learn everything about anything. When you graduate, you'll be able to balance the theatre's budget, write the dramaturgy essays, measure groundplans in alternate bases (just for fun - or if you're taping on a linoleum tile floor*), because you took accounting, English, and math, plus theatre. I just think that undergraduate studies are the time to get an excellent, well-rounded education base. Specialize your studies in grad school, and/or get hands-on experience in the real world. This is my opinion, and I'm a huge fan of a liberal arts education. I'm sure all the die-hard theatre schoolies out there will shout me down, and that's ok.
*If you're taping on a linoleum floor, like in a church basement or cafeteria or something, measure how big the tiles are. Sometimes they're 12", in which case you're good to go - you're already in base 12; more frequently they're 9", 8", or 6". As long as they're an even number, you can quickly convert all your groundplan measurements to the base of the tile measurement and then just cound tiles instead of fussing with the tape measure. In the end, you save a little time between doing the extra math up front and taping a little faster. Nerds like me think this is great. See - you should have stayed awake in algebra.