What licks are best for comping so they won't interfere with your singing?
Hi Magicbaldguy, great question! It kind of depends on the style of blues or boogie you're playing, but a great go-to lick that can be played quietly, in the groove, and understated without getting in the way is LICK #1. You can also re-voice it so that the root (usually played in the thumb) is played by the pinky on top instead. Check out the last variation of LICK #1 in "part II". That should get you started.
LICK #1 can be played in a groovy way while you are singing, but IN BETWEEN the vocal lines you can use any lick you want to fill in that space. For example if you sing "Everyday I Have The Blues" you could sing: "Everyday, Everyday I have the blues" (lick), "Everyday, Everyday I have the blues" (lick), "when you see me worrying baby" (lick), "You know it's you I hate to lose" (lick)... and so on.
Hope this helps! You can also study what others do on recordings (although sometimes it may be hard to make out the piano part). But whatever you do, come down in volume with the piano so that it frames the voice better and you have more dynamic range to play with with your voice.