VideoCommon: Header cleanup

Also remedies places where the video backends and core rely on things
being indirectly included.

Source/Core/Core/BootManager.cpp

@@ -23,8 +23,8 @@
 #include <string>
 #include <vector>
 
-#include "Common/CommonPaths.h"
 #include "Common/CommonTypes.h"
+#include "Common/FileUtil.h"
 #include "Common/IniFile.h"
 #include "Common/SysConf.h"
 #include "Core/BootManager.h"
@@ -37,8 +37,6 @@
 #include "Core/HW/SI.h"
 #include "Core/HW/Sram.h"
 #include "Core/HW/WiimoteReal/WiimoteReal.h"
-#include "DiscIO/Volume.h"
-#include "DiscIO/VolumeCreator.h"
 #include "VideoCommon/VideoBackendBase.h"
 
 namespace BootManager