The amount that you should spend on a camera for beginners will depend on the type of camera that you're looking at. As far as the best digital beginner cameras go, you'll be looking to spend anywhere in the ball park of $300 to $600.
You can find digital cameras for teens who are beginners cheaper but if you're budget allows for a model in the $300 to $600 range, your teen would be able to strengthen their photography skills better with a high quality camera.
On the other hand, a great beginner camera could be a Polaroid, which are much cheaper. You can get fantastic instant Polaroid cameras for under $100. Therefore, the amount that you spend on a beginner camera will differ according to the type that you're interested in.