There's quite a bit of misinformation and fear surrounding FATCA, but the bottom line is that it's not a big deal at all (assuming that you are OK with being 100% honest and open when it comes to complying with your U.S. federal income tax responsibilities).
If all you do is move your residence overseas, then FATCA will have no effect on you whatsoever. You could live your whole life overseas and never say or read "FATCA" ever again. Some people seem to think that FATCA requires 30% withholding on all international wire transfers or all amounts paid to persons who live overseas, but that is not the case at all. FATCA withholding only applies in very limited circumstances generally related to U.S. banks and brokers paying interest or dividends to non-U.S. persons.
Now, if you also move some assets overseas with you, or otherwise invest in non-U.S. assets (e.g., by forming a non-U.S. corporation, or opening non-U.S. bank accounts), then FATCA will be something you'll need to think about. However, it still won't negatively affect your life (as long as the assumption in the first sentence of my answer holds true).
FATCA is mainly an information-gathering tool for the IRS, and it has two parts.
First, FATCA requires some additional disclosure on your U.S. tax return--this is IRS Form 8938. So, you'll need to add a few extra pages to your return to tell the IRS about your non-U.S. bank accounts or interests in non-U.S. entities. No big deal (assuming you have your U.S. tax return prepared by someone knowledgeable in this area).
Second, FATCA essentially requires non-U.S. banks and brokers to provide information about their U.S. account holders. (I say "essentially requires" because FATCA subjects them to a punitive withholding regime if they don't comply.) So, when you open a non-U.S. financial account, you'll have some extra paperwork to fill out. Then, if you invest through fancy offshore structures, you'll need to make sure it is structured in a way that makes FATCA compliance easy (you'll need a tax attorney on board). Again, FATCA should not ultimately have a negative impact on your life.
So, no need to worry about FATCA--just enjoy your new life abroad!
(Lake Nicaragua and the island volcano Ometepe, Nicaragua, pictured.)