Taxi would be most secure, fastest and direct to your destination, approximate cost is $50. Cheapest is by subway ($7.25 including Airtrain from terminal to Jamaica Station) however there are at least six subway lines that serve the Bronx so which line you take depends on where on 179th St. you are going. Take E subway from Jamaica and transfer at 53rd St. for the uptown #6 (you can transfer to the 4 or 5 subways at 125th St.), 7th Ave. and transfer to the D subway or 42nd St. and transfer to the 1 or 2 subways.
Taxi would be most secure,