1080P is the best at the moment.
Do checkwhat is your TV's true resolution.
Is it HD Ready 720 (720x1280) or Full HD (1080x1920)
if it's the latter I'd supriced if it could not do 1080P.
And crap your image looks depends on your TV's video prosessing chip.
Zapper, Super scope and other light gun games you can't play anyway

Oh and to answer your question
i means interlaced where the TV first draws every other line then the rest, where as p draws the lines in order.
I is left over from old TV times.
P has less flicker but difference can be miniscule.