Hard to give advice on those specific shows, not knowing your taste. If you don't like bio-jukebox musicals, you can rule out Tina & MJ, but if you do, then they're definitely ones to consider. I thought Girl From the North Country was wonderful, but it wont be for everyone. It's definitely on the slower side, and it's more mood-driven than story-driven. When I saw it at the Public, I described it as Once meets Band's Visit, but with Bob Dylan.
Caroline or Change is probably a pretty safe bet either way. It's on the heavy side, but it's more of a straight-forward story driven musical - while also being genuinely great.
Can't comment on Diana, personally, but I've heard mostly bad things, and it will be available to watch on Netflix shortly.