The native Windows 8 multi-monitor taskbar doesn't have a Start button, but if you enable the DisplayFusion taskbar (Settings > Taskbar tab), it has a Start button, as well as a system tray and Show Desktop button

That option doesn't work on Windows 8 unfortunately. However, if you just want to have all new windows open on the monitor from which they were launch (regardless of how they were launched), you can create a Window Location rule that does that. Please see the attached screenshot for reference

Hope that helps!