I would consider "upcycling" some older pieces by sanding them and repainting them in bright colors. This is a relatively inexpensive way to bring fun colors into the room, and will be less expensive than buying new. Make sure you give the teen some choices.
The most important thing to teenagers is their bed- get a nice, big bed. Try quirky accessories like shag rugs, floor lamps with multiple heads, under-bed storage, and long, sheer curtains.
