Multiplexing 6x9 or 1x9

So I have a little project going down in which I am using a 6 wide by 9 tall LED matrix. However, the lights will only ever be lit with the whole row at a time (so it's basically equivalent to a column on 9 LEDs). I don't have much experience with electronics, so I was hoping someone could guide me along on how to do this in the most efficient (fewest pins used) way.

Wire 9 arduino output pins to current limit resistors to 9 anodes.
Wire the 6 common cathodes to ULN2003, drive the ULN2003 from 6 arduino pins.
Drive the anodes, drive 1 cathode low at a time to turn on a row.

If your matrix has common anodes instead of common cathodes, then a different part is needed to drive the common anode pins.

Alright, I've never used the ULN2003 before so I'm really not sure if I wired it right, but based on your description did you mean this?

Red is Arduino-Resistor-Anode
Grey is LEDs (with cathode) as well as ULN2003-gnd
Blue is cathode-ULN2003
Green is ULN2003-Arduino

Yup.
Next step - learn a schematic capture tool.
I like expresspcb.com for simple drawings for posting here.

For example, here's the start of your design.