My first Public Works Project was a fountain! I remember it because I loved it soo much once it was finally built haha. My town now has a fountain surrounded by flowers. The public works projects were a really unique way to kind of decorate your town in New Leaf and felt really monumental as it took a while to save up the funds to pay them off.
I was thrilled to get the police station as my very first public works project. I remember how excited I was when a villager suggested it to me. I chose to build it right away. It was such a great feeling to see the police station finally completed and ready for action.
It was either a bus stop or a fence. I wanted to place a bus stop right outside my station and a fence to breed hybrids towards the blue rose. Together, they both looked aesthetically pleasing.
Maaaaan, I couldn't remember. Which is funny since I can name all my first things from when I first played Animal Crossing Gamecube in 2006 x)
What always comes to mind though is the face cut-out standee, because I found a Chespin QR code for it online (Pokemon X and Y was coming out at the time)
My first one was a cobblestone bridge, which I felt was a necessity. It made it much easier to get to work (at town hall).
My first non-practical one was a face-cutout standee, although I can't remember why I built it so early on. I didn't even design any patterns for a while anyway. Looking back, it seems pointless. Maybe I just wanted to see it, since it was something new.