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I guess you could look at the Trinity version of Amarok to find most inspiration for your application.
Your layout seems ok to me, but for me, any layout would feel equally native to me. It's the appearance of the widgets and the speed of the overall application that would make the difference.
I guess minimize should minimize to the taskbar and close should be configurable to either close or still keep it running in the system tray (that would be the default action). This is how other programs have it in Trinity.
For a native Trinity application, there will almost always be the possibility to have a menu-bar, but it can also be turned off. In addition there is a configurable toolbar (large/small icons, text/no-text, button layout, etc.). It depends on whether your application really works easier with a menu bar whether it's enabled or not by default (in most cases yes, only a few no).