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This is a good question, and I think it is tough to answer because when you start playing, you learn how to properly push down on the strings with your fingers (at a specific angle/etc). When I want to mute strings, I have to go against the “proper” way to push down on the strings.
I am a fan of Dave Matthews, and a lot of his music uses the left-hand muting technique, which is how I learned. There are some fairly “simple” chords to learn that only involve using 2-3 fingers. The easiest ones involve using your pointer finger on the low E string while using it to also mute the A string… so you kind of play the E string with your pointer in a “downward/slanted” position rather than hitting the string at a sharp angle.
I found a video that shows a few easy-to-learn chords that uses this technique, and all of these chords only use 2 fingers.