If you have €650,000 to spare, Malta will sell you an EU citizenship...
If you want to do it without a big pile of capital, the easiest route is probably to get a job offer from a company that will sponsor you as a skilled immigrant, and live/work for enough years to qualify to apply for citizenship (as well as doing whatever else might be required, such as passing a language exam). Sweden is one of the easier countries, with about a 9-year path to citizenship (4 years to permanent residency, plus 5 years to citizenship), no exams. Period can be shortened if you live with a significant other who's a Swedish citizen.
If you want to be self-employed and run your own business, this route is generally much harder, especially if you aren't moving with an already-successful business. Many countries assume by default that "self-employed immigrant" means "doesn't have a job or want to get one" and/or "probably will sell drugs for a living", and treat the category more skeptically. But you can go self-employed once you get permanent residency.