How do I make a rectangle selection as precise as possible?

It’s definitely a problem with a stylus, because it can be difficult to lift the stylus (release the drag) straight up, and the slightest sideways motion can change the selection. But you should not be having this problem with a mouse or trackpad, where it should be possible to release the mouse button without moving the pointer at all.

Still, if you have this problem, another solution is, while the selection is active, choose Select > Transform Selection. This will let you refine the size or placement of the selection until you get it right, then apply the transformation to finalize it.

If you’re still having trouble editing the selection precisely with a stylus or mouse while Transform Selection is active, you can also edit the numbers in the options bar, so that you can for example enter exactly “100 px” for W, and that is how wide the selection marquee will become.

Note that Select > Transform Selection is not the same as transforming selected pixels (Edit > Transform), which alters a layer. Transform Selection only affects the selection marquee.

Also, you can use Rectangular Marquee tool to make a rectangular selection and you can set a size or a aspect ratio.

Use the Rectangle Tool.

Just to be sure:

You know that the selection slightly moves to the next whole pixel?

If you're trying to make a selection, which is rectangula, you can use Polygon Lasso tool, which creates straight lines.

If you can press 'q' to enter quickmask mode, then the selection will be a temporary alpha channel, which later pressing 'q' again will return to a selection (I can't test with a pen/tablet so YMMV).