The most common way for North Americans to qualify for residency in Europe is simply by showing sufficient income and/or assets. In every case, this is a possibility in Europe, though in most countries there are alternatives that may be preferable depending on your situation.
Without a minimum amount of provable monthly income, you could make an investment in the country to qualify for residency, typically in a piece of real estate or an operating business. If you intend to start a business anyway, obviously that’d be the residency strategy to pursue. Otherwise, an investment in a piece of property is certainly a less onerous requirement than starting and operating a business. Some countries also allow you to qualify for an investor visa by putting funds in a local bank CD.
Most countries encourage foreign investment through incentives ranging from tax incentives for large multinational corporations to providing a path to residency for a small investor.
Not all countries have this visa option, so don’t think that you can simply “buy” your way into wherever you want to live… although that is effectively what you can do in some countries.