Hi!
From my understanding, the foundation of the Fulbright program, particularly the ETA program, is promoting cultural understanding between the US and other countries, so I'd say that you are spot on in your motivations to apply. As for choosing a country, I personally had a strong attachment to a particular country, so I can't speak from experience, only what I have gleaned from others. The countries that accept a large amount of candidates also have massive amounts of applicants, so the odds may or may not be better. You should look and consider the ratios of applicants to positions as far as odds go. Here is the link: http://us.fulbrightonline.org/eta-grant-application-statistics
I would also strongly suggest finding the Fulbright Program Advisor at your school or alma mater and consulting them about deciding which program is right for you. They have been doing this more than we have, and can offer a lot of insight into choosing a program with good odds that fits your goals.
Good luck!