I usually spend most of my stamina depending on the week for the Monthly Event. This week wants you to to sweep max 60 times in plot instances. So it would be beneficial for you to do equipment upgrade materials. Next week is elite instances, so ninja fragments.
The first two weeks of any month doesn't matter but it depends what you need. If you haven't fully awaken your ninjas and equipment upgrade, go for the materials. If you are done that, go for fragments since you can refine them if you have a 5* ninja.