I really liked Legend of Korra, personally. Not as much as ATLA, mind you.

Like others said, the story isn't really a continuation of ATLA, it just occurs in the same universe. You do see a little bit of how the characters from ATLA few up and their own offspring, but it's not really the focus.

It reminds me a little of Kevin Smith movies. They all happen in the same world, but they're all their own thing.

One thing I didn't like about Korra was that each season seemed kind of self-contained. ATLA had a better defined arc between the seasons in the whole series. I think they did that in case they got cancelled and they didn't want to end on a cliffhanger, so I can appreciate that.

I liked exploring the focus of a more mature avatar growing into her role.

I've never watched the live action series, though. I'm a little hesitant after seeing the movie...

Personally, I would watch Korra first then get into the live action series, simply due to the fact that watching the same story twice in a row seems like a bit of a drag.