I've tried using my 360 on two different TV's.
The one in my room is an SD TV, but it's 28", widescreen, flatscreen (old school flatscreen, so the TV unit itself is HUGE at the back) and I frequently struggle to read stuff.
I also played on the TV in my parent's bedroom (not had a chance to try the household main TV, as mum and dad don't want my 360 in there, trying their TV was just a test) and despite it being just 17 or 19", because it is HD, it was great for reading on.
I can't afford a new TV, heck, I couldn't afford to buy a 360, I bought a used one off a mate. The reason why I have a "big" (for the room) TV in my room is because mum and dad got a 42" LCD HD TV, so I got the old one from the living room. Why should I have to pay the price of a new console, which I couldn't afford for the console, just to play my games well?
All my other consoles work fine on it (no ps3, but a Wii and various retro consoles), and I don't have any HD media. No blu-ray, no HD-DVD, heck, I don't even watch TV channels on my TV, it's purely for gaming!