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Since you're on a budget, try to find a used Canon T2i on eBay. For a lens, I'd suggest a 24mm 2.8 (since your room is pretty small). If you have an iPhone, you can use a Rode SmartLav for your mic and record audio onto your phone.
For lights, just get some clamp lights from the hardware store and plug them into a Router Speed Control (they work great as dimmers): http://www.harborfreight.com/router-speed-control-43060.html
We recently published an article about this exact topic if you're curious: http://www.videomaker.com/article/f04/17142-create-a-youtube-studio-in-your-room