I would proceed with caution.
We looked at flying them to the UK from Sweden and the price didn't include ANYTHING - no luggage, drinks, food etc. Now that doesn't bother me so much on a shorthaul, and it flew into Gatwick, which was my preference, but given our amount of luggage, we went with BA.
One of my hobbies is planewatching and I tend to pay attention to the market as well. When Norwegian announced their US services I took a look and it is extremely barebones. They will nickel and dime you to the hilt - charges for luggage, meal service, alcohol, seat reservations, pillow and blanket, etc. Also, they are flying the 787 Dreamliner which is having significant challenges with battery systems, resulting in planes being pulled from service and/or mechanical delays. The Japanese airlines have been impacted quite a bit, and Norwegian haven't avoided it either. One of their 787s when mechanical in NY around NY and it resulted in a whole planeload of passengers being stranded there (the Swedish papers took great joy in this
)
Finally - with limited long haul aircraft, if a flight goes mechanical, it could be a while before they "rescue" you, and as a low cost airline they may not feel compelled to put you up and do not have interline agreements with other airlines.
Now, this all sounds really grim, but if it is something you are comfortable with, then they could be a good option to save some cash, but certainly just be aware of what you are buying and run the sums with the "full service" airlines to ensure you are actually saving money once all the extras are added in.