When you do use the mouse to rotate, make sure you start with the cursor inside the sphere to rotate in 3D. (If you start outside the sphere, the rotation is 2D only)
A easy and quick way to view a part or assembly is to use the Compass in the top-right corner of the screen. Click on one of the X, Y, or Z labels to rotate the view to make it perpendicular to that axis. If you click on the same label a second time, it will invert the view.
For some reason, this Compass method is easier for me than use the Standard Views in the bottom menu.