You should 100% open a brokerage account at a well known US based FDIC insured commercial bank like Merril Lynch, Wells Fargo Investors, or BBVA Group.
All can be done remotely and they are the best banks for this in the world.
thank you for your answer. to be honest I was waiting switzerland, luxemburg or countries like that as a recommendation not US Are you sure that I won't be paying taxes? And can I also have a normal savings account with them?