A 2.5 mile commute will take a maximum time of 20 minutes, probably not enough time to really be sweaty enough to warrant a shower. I've been a teacher too, and commute as well. Unless you've managed to avoid working at home after work better than I, you'll be carrying papers, notebook, ect.. I'd suggest a bike (or one similar to) the Trek FX series. Plenty of gear for roads, upright position, flat bar, and racks can be attached.

I'd go for that, and racks with either paniers or bag + bungie cords. I usually ride with a messenger bag with papers + clothes, sometimes taking in clothes in advance. The messenger bag gets old, especially in the summer heat.

Edit: I don't ride in the rain, I drive instead. If you want to go the full distance with commuting no matter what, you'll want some fenders to to along with the bike too.

Don't forget the accessories + tax when you're considering the cost. It easily adds $100.00 to the cost of the bike.