Is it better to hire myself a wealth management team than to approach a private bank?

What exactly is a “wealth management team”? What licensing, references, education and track record does the company have? A banker works for the corporation which performs for the stockholders, on a quarterly basis. You need sound financial advice, not the illusion of “wealth management”. If you have wealth which requires management, then there must be trusted, ‘successful’ family friends to whom you can turn for advice.

Edit: Talk to VanGuard or similar company.
http://www.vanguard.com/VGApp/hnw/CorporatePortal