I do understand not liking Mick's singing though. He's technically pretty limited (can't sing that low note in "Ruby Tuesday" at all) and is kinda hard to take when he's doing his hillbilly voice during one of their country numbers. I actually think of him as more of an actor than a traditional singer if that makes sense (ditto with Dylan) but can't really fault folks for not liking him.
"Lady Jane" has always seemed like a failed experiment and it arguably features Mick at his worst but I like the other 2 you mentioned as well as the rest of the stuff on "Big Hits". FWIW my other favorites aside from "Gimme Shelter" are "Paint It Black" (they really should have used sitar more often- poor Brian) and "Wild Horses" (Mick's kinda annoying on this one too but it's still a beautiful song- one of my absolute favorites to play on guitar)