Given that there's entire office-based industries solely dedicated to answering these questions for others, I'm not sure how I feel about this one. Then again, being both mathematically-inclined and having the benefit of a mandatory Civics & Careers course back in high school has worked its wonders over the years. It's amusingly led to one of the only school projects that I've not only still kept after 12 years, but have been actively updating since.
Let me take a stab. Thimble: I'm a non-conformist! Battleship: I'm a kid who wants to appear strong Car: I'm an adult who is a kid at heart. Dog: I like dogs. Hat: I identify with the Monopoly guy mascot (his name is Uncle Pennybags by the way). Shoe: I like dad jokes and plan to mimic my piece walking on the board all game long. Iron: I was the last person to pick my game piece and it's either this or the damn thimble.
I realized I accidentally forgot the wheel barrow, and nobody caught. but perhaps it was not accidental. I have played between 100 and 200 games of Monopoly before I was introduced to better games and I never recall anyone picking the wheelbarrow ever.