Need some technical help (resolution settings)

So I don't ever play console games and I've learned I am a scrub when it comes to optimizing and troubleshooting the display options on these systems.

I've been playing Red Dead Redemption for the first time and I noticed a lot of aliasing, fps lag, etc. So I started messing with options and googling the best setup. I found out this game is only able to play at a 720p resolution however my XBox 360 and TV were set at 1080p or 1080i(native).

I'm curious what resolution I should set both my TV and XBox for this game?

I've read that 360s can automatically change resolutions based on your TV native resolution? Or is it the other way around?

TLDR - I have a very new 60 inch LG TV with a 1080p native resolution. What settings do I need to make Red Dead Redemption run optimally while also looking the best on an XBox 360?

Thanks

Submitted by kougrizzle | #Specialdealer Special Offer Online Shopping Store 2016