Can a US citizen who has never lived in the US, register for voting in a midterm election?
Maybe. Most states will allow such a person to vote in a federal election if the person had a parent whose last domicile in the US was in that state, or who was last registered to vote in that state. See the Federal Voting Assistance Program (FVAP) page on voters who have never resided in the US for more information. Of the first three states, alphabetically, Alabama is absent from that page, and Alaska and Arizona have different requirements:
Alaska
A U.S. citizen who has never resided in the U.S. and has a parent or legal guardian that was last domiciled in Alaska is eligible to vote as a federal voter and may vote for federal offices only.
Arizona
A U.S. citizen who has never resided in the U.S. and has a parent or legal guardian that was last registered to vote in Arizona is eligible to vote in Arizona.
Colorado extends the requirements to include other family relationships:
Colorado
A U.S. citizen who has never resided in the U.S. and has a parent, legal guardian, spouse or civil union partner that was last domiciled in Colorado is eligible to vote in Colorado.
You ask
If so, can this citizen pick any state for voting registration?
No. Since the requirements are based on the residence or voter registration of various family members, one could perhaps be able choose among several states. It's also possible that there would be no state in which such a person would be eligible to register.
Do any states make this process particularly easy if this process does exist?
I am not aware of any difference from one state to another. The application process is more or less standardized through the Federal Post Card Application. The deadline for registration varies by state, as do the deadlines for requesting an absentee ballot and submitting an absentee ballot. Details may be found in FVAP's guide.
