I like Let's Plays with "live" commentary most. Doesn't have to be livestream of course, but talking over it after recording the gameplay always seems a bit fake and weird to me. When I watch a Let's Play I want to feel like I'm sitting next to the person playing, not like I'm watching someone play while listening to someone else narrate it (if you know what I mean)
Whether the talking is strictly about the game or also about other topics greatly depends on the game being played. If it's very immersion and story-driven I'd prefer the Let's Player to acknowledge that and stay on the topic of the game with his narration. Now, whether that narration is funny or serious immersion... both can be fun to watch.
If it's a Let's Play of a game like, say, minecraft I of course appreciate it if the player talks about other interesting stuff, too, otherwise it would be quite boring.
Last, but not least, the voice of the Let's Player is very, very important. It's a bit mean, maybe, but I can't stand listening to an annoying voice (too high-pitched, mumbling, lisping...), no matter how good the narration is otherwise. A good Let's Player is also an actor in a way, so training your voice to sound somewhat pleasant is part of becoming a pro in this field
Favourite Let's Player is
Gronkh btw.