June, you are required to file taxes as a US citizen no matter where you reside and they will ask for copies of your previous tax returns during the application process. There are ways around this if you don't have your own income that goes over the current threshold and would not file a return even if you lived in the US.
When DH did DCF last year in London, I (as the USC) had to prove that I was setting up a life in the US and severing ties in the UK. I showed I'd given in notice at my job and that we'd given notice on our rental house. We showed acknowledgement letters from prospective employers in the US and e-mails back and forth with an apartment complex we were hoping to rent from once we arrived. Thankfully we had enough savings, but as someone else suggested you can also have a co-sponsor. Neither of us had a job lined up when we moved.
Good luck with it all. Overall we found it wasn't very painful, and he had his greencard within a month of landing here.