I have a 32" Sony something or other. One of the very last ones - HDMI port and does 1080i or 720p. What a find! 30 dollars, and about killed myself getting it in the house.
The plan is to have all the light gun systems hooked up to it. Being able to get 1080i out of a PS2 while having the light gun work is a challenge I have not yet surmounted.
Unfortunately, you might have trouble with light gun games. Some of the HDMI CRTs do some video processing that adds video delay. :(
If you're US based, you would probably use component video (YPbPr) to connect to your 1080i display; you can hook a ps2 light gun to the Y cable (usually green) and it should work if everything else is cool.
Most games won't work right if you force 1080i (which you can do using OPL) but the light gun will work with component signals just use the green plug as has been mentioned.
Gran Turismo 4 will output 1080i correctly, I've done that before, but the internal horizonal resolution is very low, so i actually prefer to play in 480p on my LCD, ymmv
There's Pelican brand wireless light guns NOS on eBay that work with both PS1 and PS2 games that I've so far had good luck with
Hooked up my spare PS2 and got a light gun for it. Wish i had a way to play duck hunt though.