I started in a similar way. When I made the jump to electric from acoustic I started by practicing the chords I knew without and distortion and doing scales to get the feel of the different neck, strings and tighter picking-space.

It really depends where you want to go, if you're going to play with distortion and effects then be vigilant about how you contoll them right from the starts or your playing will sound messy and undisciplined. Think about palm-muting with your pick-hand and be careful about not knocking strings you don't want sound as this will swamp the chords/notes and sound out of key.