If I'm bringing my dslr to school? Nikon D700?

Do not hesitate I go to a senior school and many many people own a dslr which they also bring to school.

1) Can I bring it with just the lens cap (so If I'm not using it I just put on the lens cap) or do I need to bring the case?

I've got a canon rebel and that thing was spensive. If I wer you I would bring the whole case so nothing can happen to it. You never know.

If your case does NOT look like a camera case and you have control of it the whole time, I see no reason not to have it at school if you work for the school paper or on the Year Book committee.

If you are just taking your fine D700 camera with you so show it off, it is a good way to get it stolen or even boosted from you.

Stick it in a backpack. Don't advertise what you own. Too many thieves out there. I carry my DSLR plus lens in backpack all the time.

It would be best if you can bring the case, though you can stick it in a backpack if you like as well if it's decently padded and you don't put it in with liquids or sharp objects that can ruin your camera.