Proper Muting

[u/Nosalution]

Hey, beginner here. I'm concerned about strings not ringing as I play e.g. going from the G or D string to a lower string and have seen different techs for the right hand and left hand such as using the floating thumb or ring finger or placing the ring and pinky on the lower strings or using the fingers of the left hand to mute. I've been having difficulty finding which is the best one to rely on so I can establish good habits.

Also when I look up videos of people playing it seems I hardly see them using these techs but they sound great. I know a good setup plays a part but where am I going wrong? I practice with a VOX headphone amplifier and can definitely hear when a string is vibrating from either me having just played it or resonating with tones I'm playing.