If your work is close to school, you can probably clean up at your campus rec center after the long commute and then ride a short distance to work without getting too sweaty. Just an idea.

I would make commuting your primary purpose in making a case to your family. I agree that you should go a model down for two reasons. First, you save money, and will have more available for lights, hi-vis clothes, and fenders. Second, your bike will be less of a target for thieves, which hunt every campus for easy pickens. A higher end bike will be a target for component theft also.

I know people who have tried triathalons on touring bikes, mountain bikes, and cross bikes. If you decide that triathalons are the thing for you, you can take a few seasons to save up and decide what is right for you. I guarantee that whatever bike you get now, you will have different needs and wants after only a few races. Get something that is primarily a commuter, and secondarily a Tri bike.