Hi Tori-Alice-8D!
If you are going to be using the Nraas suite, then the mods listed are what you will need. Out of all of these, MasterController, Woohooer, and PortraitPanel are the most critical. MasterController allows you to overstuff, Woohooer allows the sims to Try for Baby with an overstuffed household, and PortraitPanel will allow for more than eight sim portraits to be displayed on the side. Mover is only necessary if you plan to move anyone in or out of the overstuffed household.
And StoryProgression, while not necessary for the overstuffing, is nice to have just on its own merit, and gives more life to the town and townies.
I don't have any experience with AwesomeMod, so I can't tell you how that one works, but the Nraas suite works quite well with the overstuffing. I routinely play households with 14+ and, while it can be a multi-tasking nightmare at times, the mods make it all run pretty smoothly.