To help ensure people can easily move to the country best suited to them, there would be a program which all countries could choose to join. Joined countries would have buildings that citizens interested in moving away or even just seeing if there is something better could visit.
A counselor would be provided. The citizen would discuss their political, social, religious, and other wants and views, and the counselor would talk to them about the countries seeming most appropriate. The counselor would then give them guidance in how to research and choose a country as well as how the country moving procedures work.
The citizen would be given access to a computer database with political and social characteristics, news, geography, and all sorts of information about all of the participating countries, with advanced searches available.
After researching the countries, the citizen would talk to the counselor to make a final decision. If the citizen decides to go through with the move, the counselor would tell the citizen everything they need to do to proceed with the move.
The counselor would meet with a counselor from the other country to start the process toward citizenship for the citizen. This process should be an agreement between the two countries plus the citizen that would help ensure both success and safety for both the citizen and the new country. The process should be relatively quick and easy, with important records provided from the originating country so the destination country can more easily do background checks.
Some countries might only do exchanges, have number limits, or have certain stipulations on the citizens they will take, though the movement of citizens must be generally relatively free and easy.
A similar but simpler version of this service could be provided for intra-country moves, helping citizens find the best city or place within a country for them to live.