Hi ~ the taxis in JFK have a set price of $45 into Manhattan (of course, in the USA they expect tips! So make that $50!)... The AirTrain connecting to the subway is much cheaper, but it may be hard w/ two bags.
Unfortunately, the customs at JFK is very slow. It could take 45-60 minutes to clear after arriving.
Have fun! I was just in Helsinki two weeks ago to see my hockey team (Pittsburgh Penguins) play Jokerit. I had so much fun!!
JFK info