My 2 cents;
Dont try to do this on a shoestring budget, it will force you into choices you may regret later...ask me how I know.
You should be able to safe more then the 5k-10K you projected.
Easier said the done but at your age there is money to be found;
- Live with your parent(s)
- Limit your going out and partying
- Dont take holiday trips
- Watch what you spend on clothes, shoes and other stuff you really don't need
You might now be able to save another 20K so your budget is 50K with 10K for emergencies or unforeseen expenses.