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.
Renting or buying property, establishing utilities accounts, registering your car, obtaining a driver's license, registering to vote - these are all actions that indicate an intent to make your home in a given location.
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