Nice question
I really like the question, makes me think about my trips which really makes me smile.
For me the first thing I buy down in Orlando when I get there are supplies at Walmart. A couple cases of bottled water for the parks, a few beer for the room, snacks to bring in the parks like granola bars, crackers, beef jerkey.
First thing I buy every time in a park is a bit dull, but it's the same with every park... locker rental.
First real purchase is almost always food of some sort, usually a breakfast item if at HS (Farifax Fare after getting a fast pass for TSMM and riding it, then riding both ToT and ARR) , AK (Kusafiri Coffee Shop after getting a fast pass for Everest and riding it once) or Epcot (Sunshine Season Food Fair after getting Soarin' fast pass, and potentially riding it), MK is a toss up between having a baked good (donut or something at the bakery or waiting a bit for a funnel cake usually after getting a fast pass for SM and riding it).
Souvenirs happen whenever we see something of interest that we really must have, it's never the same thing, but often it's t-shirts, or a ball cap.