LLC for real estate investment
When you purchase a real estate property in a given state, this would be the state where the LLC, holding this property, is to be registered. You could either own this LLC directly, or form a holding company (LLC or Corporation) in one of the incorporation heavens.
I would recommend you to consult a US accountant to discuss which strategy would be best for you. We work with a CPA firm that provides our clients with free tax webinar for Non-U.S. entrepreneurs and I recommend you to take advantage of that resource.
As far as bank account opening goes, the regulations in the US make it very difficult and risky for third parties to offer this service, so the best solution is unfortunately for the company owners to travel to the US and open the account in person. We can however help you with all the documents that need to be brought to the bank.