Muting with the right hand is the best way. But with new strings when the noise is more prominent, I turn down the treble too for this reason- cuts down on the clanking noise and finger noise. And flats will help, but you might not like the sound as much. Roundwounds have crevices or small spaces between the windings that catch your finger, resulting in excess noise. With flats, the windings are close together and result in a smoother surface, so they are naturally less inclined to create noise from your finger sliding across them.
Also, I agree with the two comments that said it's kind of part bass playing- and if you're a beginner, I would just focus on playing for now and you will eventually gain more control over the sound as you progress. Don't sweat it too much.