Right settings for the voltage ripple measurement?
Don't worry about the 10x vs 1x probe, you can make good measurements with either.

Here's a technique that I recommend:  Wind some bare wire around the barrel and tip of your scope probe to make a "socket" for the probe as shown below.  Solder the two ends right across the output capacitor.  If you have a diff probe you can try that as well for comparison, but this technique has always worked well for me.  Try also comparing with your short spring ground clip and you'll likely note that this method gives a better measurement.