Four pax + luggage? if large suitcases, you might not fit in one taxi. Still, plenty of them in the taxi rank outside the station. Taxi should cost you around 20€ per taxi, tops, including supplements.
Anyhow, your journey is as easy as it gets... You could take the metro (L3 green) at the same station (Sants) and stop in Liceu, it's barely 6 stops (~15') to where you're going, the Palau Güell is around the corner.
Check https://www.tmb.cat/en/barcelona/metro/-/lineametro/L3 . If you get a T-Family card (8 journeys, multipassenger), it'll cost you 11,05€ for the four of you -and you'll still have 4 extra journeys for other trips you make while in Barcelona: https://www.tmb.cat/en/barcelona-fares-metro-bus/t-familiar