I didn't move yet, but I just made a trip over on Iceland Air, and I will probably fly them every time. If your dates are flexible, their booking tool shows you all fares over a 2-week time period, which is very helpful. It was the least expensive flight we could find, I was allowed 2 checked bags at no fee at all, and more for a fee if necessary, as well as a carry-on bag and a personal item. This was the first time any airline insisted that I put my camera bag inside my purse so it was all one personal item, but that was no loss as I always allow for that possibility anyway.
The flights all go through Reykjavik, and Iceland Air allows you to have as much as a 5-day layover on a single ticket price, so if you wanted to, you could spend a day there and see an amazing place few people have. I had a 9-hour layover (intentionally) and left the airport (you're allowed to leave without claiming luggage that is checked through to your final destination) to go to the Blue Lagoon for the most amazing swim of my life.
As you get on the plane, they hand each person a bottle of water, and honestly it was the best water I've ever had. They also give each passenger a pillow and blanket (waiting for you in your seat) and the blankets are wonderful. Thin, light, but incredibly warm. I brought 2 home with me.
The downsides are that all the food on the plane is for a fee, and the movie selection was not huge. Several of the movies were Icelandic. Also, Keflavik airport is quite small and shuts down completely (as in, all the stores are closed, cafe's closed, and you might find one person to ask a question) in the middle of the day when no flights are due for a while. If you aren't one of the first few people to your gate, you won't have a seat while you wait. I won't arrange for a long layover there on a regular basis, but despite all this it was the experience of a lifetime, and definitely worth doing again at some point!