How do I cleanly remove these parts of an image?

The important thing to remember is that Photoshop has a very wide range of tools and command to select things. If the gray is important, then one way to do it is to select based on gray, instead of having to draw it yourself. One way to select by tone or color is to use Select > Color Range, sample the color, expand the Fuzziness to include enough of the variations in gray, then take that selection and convert it to a layer mask.

One thing I forgot to do is set a better  blending mode for the pattern layer. That would help it merge better with the shading in the joystick image.

That approach might work well enough for a mockup. If you are trying to be precise enough to print from, then instead you will want to outline the buttons and such, but instead of fighting with the marquee tools, consider creating a vector mask containing paths drawn with the shape tools (e.g. Ellipse, not Elliptical Marquee) and Pen tool. This takes more training if you are not already familiar with editing vector paths, but is much easier to edit both precisely and rapidly, and is resolution independent.