How to play the mandolin smoothly?

I play the violin and the guitar, and I whipped out my sister's old
mandolin the other to mess around with it. Since the strings are
doubled and really close together, I have issues pressing down hard
and not touching the other strings with the fingers i'm using. Any
tips on how to hold it or arch my fingers or finger placement that
will help it just sound better and not all buzzy and choppy?

Thanks!