You simply do:
widget.menuMarket->setStyleSheet("QMenu::item:selected{border:1px solid red;}");
That's the right place to do it if you only want one specific menu to behave like that. (I don't see why setting that in Designer wouldn't work. Give it a try. But I'm not familiar with it myself.)
If you want all your menus to have the same style, do it at the QApplication
level, in your main
or some other piece of code that runs once at startup.
QApplication app(argc, argv);
// ...
app.setStyleSheet("QMenu::item:selected {border: 5px solid yellow;}");
// ...
And you can combine the two. The stylesheet you place on a specific widget (first example) will override the global stylesheet (much like CSS does).
This works the same in Qt4 and Qt5, though Qt5 might have more style options.