How can I avoid clicking quite so much?

You can bind all movement and actions to keyboard keys. You can bind "Move" to a key, and it will move directly to where your mouse is pointed without requiring clicks.

You will still have to use clicking for your primary and secondary skills, but if you use a lot of clicking and holding to attack rather than repeated clicking, you won't have to click too much.

There is no WASD option.

You can hold you mouse button down for any continuous operation. For example, walking through an empty area requires a single, albeit very long, click. The same is true for attacking, although you will sometimes need to click on new targets. However, there are some attack over time skills that don't need a target selected. For instance, Rapid Fire for the Demon Hunter and Ray of Frost for the Wizard are like this. Additionally, holding Shift (I think) forces your attack, allowing you to just aim and not explicitly target enemies.

One technique that is quite popular and which I found improved my reaction time a bit, is what's starting to be referred to as 'Stutter-Step Casting'.

Essentially, rather than rebinding anything you simply hold down the mouse button to keep moving, tapping or holding shift as needed to plant momentarily and take shots. This helps you stay moving, reduces wear on your mouse and wrist, and, in my experience, improves reaction time a little bit. It also prevents the whole 'moving when you mean to attack' thing that you described - you will never move when you meant to shoot if you do so by hitting shift! The main downside is that occasionally attempts to use other skills can be blocked out by this, so remember to release your mouse button if you want to use a different ability!