Annyeong! 안녕!
Do you have a plan for going to Seoul? but do you know how to go to Seoul? it is one of a problem(?) going to the city where you want from the airport I also make a plan first going to the city from the airport when I go to trip so I would tell you how to go to Seoul or other cities from Incheon National airport 
- Taxi
honestly, I don’t recommend using Taxi in Airport because that is expansive and some of bad Taxi drivers do overcharge to travellers who from abroad
but your group is about 3~4people then using a taxi would be a good choice
it starts at about 40,000 won (40 dollars, To Mapo gu in Seoul) ~ 70,000 won so do you think the taxi driver was doing overcharging then you say first “I will report to Police office about this” then almost fraud taxi driver back money you, even they still do then call police then police will arrest the driver (Korea Tourism Police number is 02-700-6278)
- Bus
Incheon airport has Bus for travellers too also bus company services at midnight too so you can use bus any time
here is information about bus lines and you can check the price! : https://www.airport.kr/ap/en/tpt/busRouteList.do
also you can use a bus to go to other places (Busan, Daejeon, Gwangju…)
- Express Train
I recommend using the Airport Express train because it’s the price is reasonable and fast to Seoul and I think it is most comfortable for me
also, it has a restroom and wifi!
Adult : 9,000 won / Kid : 7,000 won
Group(over 3 people) : each 7500 won
if you have a plane ticket (Korean air, Asiana air line, Jeju air line, T-way air line, Esta air line) then 7500 won
over 65 years: 7000 won
if you used this train before 15 days: 7500 won (but you should show them the ticket you used)
FREE WIFI and Free Restroom
4.Metro
Metro’s good point is Cheapest even it isn’t comfortable and slow much them which I introduced but if you want to save your money then it would be a good choice for you
price about 1250~2000won
more information about AREX: https://www.arex.or.kr/main.do
Well- how was post? sometimes I use Airport metro to meet my friends who came from overseas!
I hope it would help for your Seoul trip
If you have any question comment here I will replay ASAP!