The teleport is only on the very first hit in the sequence. If you continue to use this skill, every third hit (after the first) will teleport you.

Even so, the mobility it grants you is absolutely insane. You won't have to manually move in combat again.

Just about the only thing you can do to speed up the skill switching process is to right click on the skill you'd like to change. By doing this you'll jump directly to the skill selection for that key, bypassing one page of the menus you'd normally click through.

This is the only way to speed up the process of changing skills. There is no other way to automate or hotkey skill selection in Diablo 3. It must be done through this menu.

Any 'out of the box solution' would require, at a minimum, the use of some form of third party macro or automation software, a clear violation of Diablo III's Terms of Use. While such violations are not always detectable or acted on, the possibility of action against your account and revocation of your license to play would give me extreme pause in considering any other solution.