Buttons are the basic standard items to collect and trade.
I have a wall in my office full of FIRST buttons.
I also have Frisbees,
Bandanas ,
Pens & pencils,
Note pads with team # & name,
Small chunky note books (very useful),
Candies (ate them),
Noise makers (you name it.. I’ll gotten it),
Costume jewelries,
Hackie sacks,
ID neck straps (useful),
Team canvas bags,
Plastic swords,
Tee shirts (tons of these),
Devil’s pitchfork (from that crazy NJ team),
Magnets of every shape and theme,
Stickers big and small,
Eye-patches (from the pirates),
Plastic money,
Tissue packs (comes in handy),
Stress balls of many shapes,
Yoyos big and small,
Form rockets,
Moe Sticks (a collector’s items),
Maps (yeah),
Cans of Soda,
Makeup bags (that’s right),
Caps,
Blinking LED lights,
(and this is just stuff in my office desk!)
One team I Project Manage sometime cruises the 99 Cent Store or Odd-lots for bargains. One time they purchased all the canvas bags from one store for 50 cent each.
My all time favorites are hand-made custom team pins. These I treasure.

Btw- we are experimenting with plastic chocolate molds and resins to make custom pins this year. Anyone tried this before?