Some arcade-y faves of mine:

Gradius V: a classic horizontal scrolling shooter, it gets hard quickly! (This is the game series the Konami code originates from)

Neo Contra: a twin-stick shooter inspired by B-movies, also kinda hard, and incidentally also a series that made the Konami code famous.

The Red Star: a bit obscure I think. It’s a twin-stick with both shooting and melee. I like the girl’s fast melee moves a lot, you need to use combos to juggle your enemies. I think this one got a bad reception because it arrived quite late in the life of the PS2 and was a bit underwhelming graphically.