In distinguishing socialism from communism the issue of the amount of allowed private property comes up.
The amount of private property needed would surely depend upon where a person lives, what job they do, etc. I would think we would all need a few of our own clothes, toiletries like comb, tooth brush, razor, etc. We might need a watch and cellphone. Until recently we would need files and notes and specialist's books (in my case for my research and the textbooks I teach from). With the advent of e-readers like kindle we might instead be able to access books and papers not found in our local libraries. In certain remote locations one might need private transport. We might also need glasses (as I do), hearing aids, etc. We would all have a few personal items like pictures of loved ones, etc.