first shopping of the year; first purchase of the year
Refers to the first shopping trip or the first item bought in the new year, often associated with New Year's customs.
It's a family tradition to go for the first shopping of the year on New Year's Day.
My first purchase of the year was a lucky bag.
Compound of 買い (kai, 'buying', the continuative form of 買う) and 初め (zome, 'first', rendaku form of 初め). Follows the pattern of other New Year's 'first' activities like 書き初め.