Seoul runs on its subway, and the fare has moved recently enough that a lot of published advice is out of date: 1,550 won on a transit card since 28 June 2025, not the 1,400 won still quoted in plenty of guides.
These guides cover the decisions in the order you meet them. Getting in from Incheon comes first, then which card to buy, then the day-to-day question of when the subway stops being the obvious answer and a taxi starts making sense.