I had to furnish a TON of documents (Europeans LOVE paperwork, would probably declare war on the USA if we suggested they adopt our "Paperwork Reduction Act" , but got my residence permit. It is different even within a single county, let alone country or the whole EU. I hear Estonia is happy if you all you do is dump a modest sum of money in a bank account there, and I doubt they expect anyone except someone from Finland to master their language.
I first tried in the county seat of the town where my wife has her primary residence. They made me jump through hoops and at the end of the process gave me the wrong visa. In Germany (I promise I'm not making this up), when you move somewhere, you must register your residence with the police, and your phones will probably be monitored. Mine are (ex-Mossad pals have detection equipment that can determine this). If you move, you must tell them where you moving to, and then register with the police in your new town as well. I had to de-register myself when I went to America for the summer because the visa they gave me was not the residence visa I had requested, but a business visitor's visa for an extended 90 days. I had to re-register when I got back.
Then a "foreigners' bureau" opened in the town where my wife's residence is, and the people there were far more competent. They asked for the tons of documents all over again, but actually knew how to process them. I got my residence card within two months. It was good for three years, but when I applied for renewal, the new card was for permanent residence.
It helped that I was married to a German citizen, of course, and that I would not be asking for any benefits from their government, although they found that highly suspicious (it rarely happens).
What I had to furnish, among other things:
Marriage documents (we were married in the USA) with an officially sanctioned translation into German.
Proof of employment with proof of salary. It was not an issue that my employer was an American entity, paying me in the States.
Proof of health insurance.
Proof of good health.
Proof of financial solvency (bank statement from my home in Dallas was fine).
Proof of German language proficiency (my oral command of German was sufficient, so I didn't have to take any tests).
There were plenty of other things, I just don't recall them all offhand. My wife, a social worker was furious with them, as they demanded way more from me than they demanded from Russians, Afghans or Albanians showing up, asking for free money, apartments, cell phones and cars (which they often as not got for the asking). And yet they made me go through the wringer to get an official residence. Not too many American civilians apply for German residence out of the blue. The authorities here are not used to it, and they often don't know how to react when it happens.
Last time I came back to Germany, I flew in nonstop from Atlanta to Düsseldorf. When I got to German immigration, I showed my passport with my residence card. The woman at the immigration checkpoint studied my dox, and remarked that not too many Americans showed up with a residence permit. I remarked that my wife was German and wanted to live in Germany. The border policewoman remarked that she would rather have gone to the States. I explained to her that in such cases, the woman was always right, and we men had no say in the matter. She smiled, approved of my observation, and waved me through.