I don't have much direct experience with BC in XBone. But, my understanding is that most games do see a performance boost. But, no games run at a higher resolution unless they were specifically upgraded to do so, and the ones that were upgraded were only upgraded for XB1X. So, on a low cost X1 you won't get that resolution.
One game from your list that I can comment on directly - RDR. I never played it on 360, so I can't give you a comparison. But, on XBone it did run very well in general. It was one of the few BC games I played, and I recall that I was impressed with how well it ran.
With that said, since MS has said that new games will be XBone compatible for a couple years, and because you want to play Halo games, why not buy and XBX? You'll be able to play all of the Halos in their upgraded glory, and play Infinite. You'll also get the benefit of being able to play the other MS exclusives that you've missed. Even if there aren't that many, when you add that to the great enhanced BC, and the excellent Halo experiences, it's probably worth the $225ish you'd pay for a used X right now.
As a huge Destiny fan myself, I can tell you that Halo games are must-play. They have nothing to do with Destiny, and they're quite different games. But, that excellent Destiny gunplay comes from Halo. If you've never played them, you're missing out. Personally, I own all platforms. But, Halo tends to keep me as XB first, because I don't ever want to miss playing one.