Sofia Airport: Take Metro Line 4 (Yellow) from the station outside Terminal 2: it is the clean, cheap default, roughly 20 minutes to the central Serdika area according to the airport (some traveller sources quote up to 40 minutes), for about €0.80. If you land at Terminal 1, use the free Terminal 1–2 shuttle first. Bus 84 is acceptable for Orlov Most/Sofia University (30–40 minutes), but is traffic-dependent. For a late arrival or heavy luggage, use only the official OK Supertrans rank/desk; expect about €15 to the centre and ignore anyone soliciting rides in arrivals.
Sofia Central Railway Station: The station is on Metro Line 2 (Blue), one stop/only a few minutes from Serdika and the historic core. It is also beside the Central Bus Station, so do not pay for a taxi merely to change between rail and coach.
Central Bus Station / Bus Station Serdika: Use Metro Line 2 from Central Railway Station next door for Serdika and the centre. The international Serdika bus station is the smaller facility between the rail station and main bus station; walk rather than hunt for a transfer.