Hmm, it takes a while to get used to the rig system. I use both the R and the 2xR. It depends on different situations and what effect I want. 

A big thing to have in mind is the point of view where you’re working with the pose. Depending on where you’re looking at the rig, the R can do one thing, or it can do a completely different thing. For example, when I want to bring the arms down I press 1 to look at the rig from the front view, then press the shoulder joint and R to bring it down. If I were to do this on the side point of view (by pressing 3) then pressing R would not bring the arms down, but forward or backwards instead. SO I would have to use 2xR. 

Also, 2xR I use more to fix and make things look more natural, but with caution, because too much rotation makes the rig look twisted, in those cases, if I can’t find another way to move the rig so that it doesn’t look twisted, what I do is I use G, but agan, with a lot of caution, because this one can really mess up the rig. 

And I guess, to make it look more natural I try to look at references when making poses. Now that I’ve gotten used to it I can kind of see things better in my mind, but at the beginning I had to use references that showed every single thing for the pose, like if there was a hidden arm because of the angle of the picture, I would freak out. Or I also try making the pose myself. That usually helps for a quick checkup.

Edit: for lifting up the arms and not having them look super twisted, you should try rotating the shoulders AND the joints right under the neck, I think they’re the collarbone one? Tweak both these joints until you get something that looks acceptable. It’s a messy process.