Here is a question, how many of the Season 2 cast bonded with an item like the S1 cast did? Betty had her riot helmet, Vance his bat and Letty the dumbbell. Jimmy obviously had the phone which got him kicked, I guess you could point out the painting for TJ, but he didn't really have much interest in it beyond a single evening because Jet ran up and immediately took it to the basement. With Tay I could point out three things, her yarn, her mug and then at the end her sunglasses but she didn't really seem to care when the yarn was destroyed, even to the point saying that she was happy to take a break from crocheting, her mug was always present but that was because she was pounding water to stave off hunger. The sunglasses she wore on her forehead most of the final week but I felt like that was because she was told it was "beach week" not "beach day" so she kept wearing the beach garb beyond the single night. Trish and Shinji didn't seem to attach to items either unless you want to point out Trish hiding in B2 most of the week before she was eliminated.
Season one had the following, although I might be overlooking a few. Most items associated with the fish I've noticed usually play a big part in their arcs. Vance used his baseball bat to break Letty's shit, Jimmy was eliminated due to the phone, Jon almost destroyed Letty's passport because of his Bible, Josie used Queso during the willy wonka skit, etc. This isn't always the case, but I find it interesting.
Simmons: Harmonica
Vance: Bat
Jon: Bible
Mauro: Halo Book
Josie: Queso or Duck Toy
Damiel: Real Phone
Sylvia: I don't recall Sylvia having any item. I guess her overuse of make up might count? Maybe the Uncle Ted book?
Letty: Glasses. Although, this might not count to some because she literally needed them to see.
Season two (still up for debate)
Jimmy: Fake Phone
Cole: Sunglasses
Tay: Probably the yarn, although I think she never really had a deciding item. One could also argue her panties just because of pantygate and her giving them to Frank being two notable things she used them in.
Summer: Never really had an item.
TJ: His hair. Was really the only eye catching thing about him during the first half of the show. Most TJ fans probably consider him losing it a "changing point" in his very artificial arc.
Megan: Never had an item. Closest thing I can think of was the robux gift card.
Brian: Trish and CK (lol)
Trish: Nothing that I can recall.
JC: Closest thing I can think of were the casino chips, only because she was tasked to steal literally all of them.
Shinji: Nothing that I can remember.