I'm told by others and read in Looking for a beginner's tutorial to using the API that I need "To Get A Key!" but when I then visit https://stackapps.com/apps/oauth/register I'm stil uncertain how to proceed.
If I only need a key what is the shortest route to success without causing troubles for me, my app/script or others?
When you click the Register link you're presented with this webform:
Once you have registered an app, you will need to generate a key. You can do this in the API Keys section on your app's dashboard page. Use the "Generate new API key" option and the key will be displayed in a modal. Be sure to copy the key, since this is the only time the full key will be shown to you!
On the dashboard you can rotate a key (replacing the old key value with a new one), delete a key, and create additional keys if needed.
Enjoy your new app and key!