I want to say that their objects represent something about them. Like Naoto's keyboard and mouse is her analytical nature? Shinjirou's Rubix Cube is his complex nature? And Minato's hair dryer represents his... perfectly maintained hair?
I thought it was the characters just holding household item and getting ready for some big food feast or something... then I saw unicycle and that went out the window as well...
I was thinking if anything the artist was just looking around his house and started drawing stuff. That makes the Junes basket a bit out of place though.