Have just spent three days in beautiful rainy Helsinki and loved every minute.
We had Vodafone NL sims in our phones as HEL was our last stop on way home so can't advise on sims in HEL airport. Most EU sims roam all over the EU, so if you have sim for rest of EU, it will work ok in HEL.
Train is 5 EURO one way: helpful rail person assist you at vending machines in walkway to station.
Trains run every 10 minutes or less.
Journey takes ~30 minutes. (as a Melbournite, the efficiency makes you weep!)
Also install Helsinki Transport app - use to buy a one day pass on their tram network. Ticket is a QR code on your phone; we never saw a tram inspector and tram fanatic I am I rode the trams all over the place.
Terrific tram network. Download and use their network map.
1. Go see amazing rock church - tram #1 to Sammonkatu - approx 10-15min by tram from city centre.
2. Visit white Helsinki cathedral with square in front (plain inside)
3. Then walk 10 mins east to Uspenski Cathedral - Finnish Orthodox church - beautiful inside.
(3a.) From there walk to harbour. Depending on how you're going for time, take ferry across to Suomenlinna (ferry included in your day pass). Ferries every hour on the hour return on the 20 minutes (approx.). Plan on 90 minutes round trip.
4. Have lunch at Old Market Hall on Eteleranta, near harbour - we had an amazing seafood soup in there at the "Soup Kitchen"; Qatar flight attendants were eating there as well!
Tram #4 back to station, 30 minutes to airport, then 10 min walk to check-in area.