You can't just choose a state to vote in without establishing residency. As a US citizen living overseas, your last US residence address is your "voting residence address" - that means it is your address for voting purposes. To establish a new voting residence address you must live in the new location with an intent to make the location your home.
Each state has its own requirements for establishing residency for voting purposes. You may find this site useful: http://www.infoplease.com/ipa/A0781452.html