I have been doing this for the past year and a half (Canadian Citizen, working in Finland). It has been great, but there are some things that you need to watch out for.
- Ensure the countries have a double taxation treaty in place, so that income you claim abroad does not have to be claimed at home (or rather you have to claim it, but not pay tax on it again)
- Residence permits for self-employed persons can take a long time in some countries. For example, Finland has two national languages, and I decided to apply in the minority language (Swedish) because I was studying it. It took nearly 5 months to get the residence permit, partially because of the extra bureaucracy involved with doing things in the minority language.
- Cost of living is a huge issue. Choose a country where you will benefit from the currency exchange (harder with the US dollar lately). I am earning Canadian Dollars, living in Euros, and it hurts.
I do not think that citizenship should be an issue, though, unless you obtained your citizenship recently. If you are a natural born citizen, living in another country under a residence permit should not affect things.
I hope some of what I said helps.