what kind of workout should a defensive nose tackle work on and what type of extra protection should one have on the field?

See if your team is having workouts. If they aren't just do basic stuff to build strength and explosiveness then do other active stuff. When I was in school I caddied and then found a pickup game of something (baseball, floor hockey, basketball, whatever). Between lugging golf bags and running in whatever game I could find, I was in decent shape when football started.

Your school will get you all the equipment you need (except maybe shoes and mouthguard) but you might want to get forearm and hand pads.

Your coaches will be happy to help you with any type of workout you need to do that will enhance your performance on the field.. They see you in practice every day and know what your strengths and weaknesses are.. Have a talk with them.. Good luck....

My best advice for you this (and every) offseason is to eat healthy, exercise by doing weight lifting, and either jogging or going for a long run every day. If you do these things, you will get faster, stronger, and into better shape, which will greatly improve your chances of becoming a successful, top notch nose tackle in football.