Two weeks from Tibert to Beijing is unrealistic for backpacking. You will be spending most of your time riding a train. What I am trying to say is that the train from Tibet to Beijing will take up to 5 days alone, out of your 14 day trip.
I would suggest that first, you map out the cities to visit in conjunction with the rail lines inside of China. Plan on starting in an international city to obtain a flight there first. As far as I know, there are no INTERNATIONAL flights to Tibet. So plan on flying into Beijing first, or a city nearer to Tibet, and then taking a train.
Here are some good websites to hep you select a train route. They are in English, so it will make getting a ticket and planning much easier for you.
http://trains.china.org.cn/
http://www.travelchinaguide.com/china-trains/
http://www.chinahighlights.com/china-trains/
http://cnvol.com/
Here's a railway map of China. It will really be a great help to help you plan your trip.
http://cnvol.com/china-railway-map.htm
Hotels in China can vary from really cheap to outrageously expensive. I like Hostels, and if all you want is a bed in a shared room, it can be as cheap as $us 3 a night. Hostels are no frills, but can also be nice and clean and a great way to meet fellow adventurers.
http://www.yhachina.com/
http://www.hostels.com/china
http://www.hostelbookers.com/hostels/china/
http://www.hostelworld.com/hostels/China
Have fun!