Good question and can be done numerous ways depending on your comfort level and predelictions.
For both 9P and Log Cabin blocks to be successful, you need contrast in Value of your fabric. Since you do not have a large stash, maybe you just need to get a few Fat Quarters to add and make it look more scrappy.
I am one that can do all the cutting and then pull from and bag and just sew together. For these blocks I would have two bags or piles. One for light fabric and one for dark. The mediums can go to either one. Not everyone is comfortable with that. So maybe cut a few pieces and put some together.
Whatever I do though, if it is new block, I cut enough for one and make it. Then if I don't like the placement or some fabric in the block I can make a change before I cut up all my fabric.