In the 2005 documentary Romántico, Carmelo Muñez Sanchez asks about applying for a visa to come to the United States and is told that in order to be accepted he needs proof of his financial stability in his home country. Though he owns his own home and has a semi-regular source of income, he says that it is unlikely that he will be accepted.
You seem to be mixing up two different things here.
The bit about financial stability in your home country is only relevant to visitor visas. It's not really financial stability they're looking for, but ties. One of the common routes to illegal immigration to the US is to get a visitor visa and simply not go home. If you're young, from a place in the third world and don't have strong ties to home you're very unlikely to get a visitor visa. If you're older, established and from a first world country a visa is usually easy to obtain but generally not even needed--most such people are eligible for the visa waiver program. (It's not all because one of the US requirements for the visa waiver program is that it be reciprocal--if a US citizen requires a visa to visit the country then it's citizens require a visa to visit the US.)
If you're somewhere in between these extremes it comes down to convincing the official at the consulate that you're planning to go home afterwards.
Immigrant visas are a totally different matter. They don't give a hoot about your finances in this case unless the person who is sponsoring you doesn't have enough money. Note that all US immigrant visas except the diversity lottery require a sponsor in America. Other than for the spouse and minor children of a US citizen these are all capacity limited and have waiting lists that range from months to decades depending on exactly what category they are in (parents are shortest, adult siblings are longest) and what country the person is from. (Most countries have the same waiting list but a few countries with large numbers of applicants have longer waiting lists.) One can only sponsor their first degree relatives.
There are also employment visas that have the possibility of turning into permanent residence. In this case the employer is the sponsor, although without the financial obligations that apply to family sponsorships.