480p 1080i question

[scarpi]

Being new to Blu-ray, I have a question that some of you probably can answer. I have a new Sony BDP - S2000ES player. It is connected to a Mitsubishi 65 inch CRT HDTV that I bought in 2001. The best connection this tv has is component video connections so I had to connect my new blu-ray player via component video. The tv also has settings for 480p or 960i. As you know the Sony player can be set at 480i, 480p, 720p, or 1080i, via its' component outputs. When I set the player to 1080i I don't see any picture. But with it set at 480p or 720p, I do. My question is what setting do I set on the tv and blu-ray player to get the best video results on DVDs and any new blu-ray discs I buy? And yes I plan on buying a new tv with the HDMI connection in a couple of years. But this tv has a fantastic picture and works great.
Thanks for any info.