The blue archive's fandom wiki kept a detailed list. Generally most schools with clear national/country reference or aesthetics will focus on weapons based on said country, like Germans (Gehenners), British/Israelis (Trinity), Chinese (Shanhaijing), Soviet/Russians (Red Winter), and Japanese (Hyakkiyako), but there are some that didn't follow the national aesthetic, like say:
- Millennium, who prefers more modern to outright futuristic looking firearms (say, H&K G11 or Keltec RFB, even a railgun)
- Valkyrie, who is separated between general law enforcement style stuff (Kanna and the police), spec-ops tacticool gear (FOX Squad) and WW2 stuff from the Finns (Rabbit Squad)
- Highlander, who prefers anything wild-west, so going for stuff like Revolvers and Shotguns and not necessarily country-focused
- And then you have cases like Abydos and Arius, who probably only uses what they can get, so theme and aesthetic choice aren't the primary focus so long that it works
That said, it's not like they follow this bit 100%, though. There are Millennium students that uses low-tech firearms, and not all students from those school adhere to the country/national aesthetic that can be considered as plot reason (Azusa, for one) or just because they want to be quirky and different from the get-go.