New fangled multi-touch trackpads and Gnome actually work really well. You can, with some practice, use a trackpad with multi-touch (such as a Lenovo T440) without having to click.
To click, tap on the touchpad.
To double-click, tap twice.
To drag an item, double-tap but don't lift your finger after the second tap. Drag the item where you want it, then lift your finger to drop.
If your touchpad supports multi-finger taps, right-click by tapping with two fingers at once. Otherwise, you still need to use hardware buttons to right-click. ...
If your touchpad supports multi-finger taps, middle-click by tapping with three fingers at once.