Some moveable shapes I often use:
For m7: E.g. F#m7 2X2222; Gm7 3X3333, etc. (bass pressed with middle finger and bottom 4 pressed with ring finger)
For 9: E.g. B9: X21222; C9: X32333, etc. (bass pressed with middle finger, then index finger, bottom 3 pressed with ring finger)
[See how seemless F#m7 in this way goes to B9]
For maj9: E.g. Dmaj9: X52222; Ebmaj9: X63333, etc.
For 13: E.g. A13: X02002; Bb13: X13113, etc. - often used on V (fifth harmony)
(read more
here)
Does this make sense to you?