One of the most popular ways to come is the E2 visa option. This is where the person either establishes their own company or buys an existing business.
The investment must be substantial, and would be dependant of the type of business.There is no set figure for what is substantial. What is needed for one type of business is not necessary for another. If you establish you own business you will need business plans, forecasts etc for several years. The I come being generated must be more than marginal meaning more that to simple survive on in the USs.
Most expats tend to buy an existing business so as to gain a visa to move to the USA. Again this is normally the E2 but instead of starting from scratch, they buy any business for sale, favourites are normally pool companies, gardening, property management etc. The down side to an E2 visa is it requires renewing every 5 years and does not allow permanent residency ie green card.
If you find an employer willing to take you on, then they can sponsor you and that can allow for a green card.
Likewise if you have a large sum to invest you can apply for an EB5 visa, however changes last year basically doubled the amount required. Again it gives a green card. The a,out now however is around 1 million dollars.
Student visas can allow you entry but you need to attend a college or uni. So really you would need to think hard about what you want and what you can afford.