Andante means at a walking pace, Con means with and Moto means movement. So it basically means... At a walking pace with movement.
So you would probably have a slight accent on the strong parts of beats and then no accent on the down beats as to accentuate the idea of movement. A slightly more loud upbeat followed by a slightly softer down-beat. It should just have a general effect of movement at a not brisk pace.
That would be my interpretation if I ever saw such a character indication for a guitar score, the piano players in the audience here may have a view more specific to the piano.
And take note Andante con moto is a character indication, not a tempo marking.