2.5 miles, absolutely any bike is sufficient. Just make sure it's safe (brakes work, chain won't slip off, chain ring won't grab your pants and cause you to fall).

Unless you are riding on dirt/gravel roads, rain does not add ANY wear/tear to the bike.

I agree with other posters, I have an 11 mile one way ride and I would ride my bike even if gas were free and cars were given away. I get cranky and my blood pressure goes up when I don't ride (seriously, I have to increase my BP meds)