Hi @jocqua!
Definitely start with The Last Airbender! Unfortunately as @coinsandchains pointed out it's off of its Amazon Prime run, but it's well worth purchasing digitally or physically. Best to get the unadulterated version before they attempt the live-action Netflix reboot in a few years while you can.
The Legend of Korra is different than The Last Airbender, so keep a healthy mind going into it. While it follows The Last Airbender, it's an entirely different show with a different period and different problems. Less "world-ending, genuinely evil, voiced by Mark Hamill" bad guy and more "people who think they're doing the right thing" bad guy. Rather than seeing how Korra's going to impact the world's problems, watch the show for how the world's problems are going to impact her. It will make your viewing experience more positive.
Cheers to you!
~ Mako
Great suggestion, @makowrites! I'll keep that in mind as I go into it. I legitimately have been listening to the sound track on repeat though. I think it's really fantastic. And I love those 20's style songs you were talking about that pop up. They're so good!
Also available on iTunes! I just found out. Honestly I'm gonna check with my brother first because he might already own them hahaha He loves this kind of stuff. Thanks again!