Unless you are obsessed with getting the best photo ever and can afford a private photography tour, I’d recommend the bus tour from Reykjavik Excursions over a private or semi-private Jeep tour. The guides are knowledgable about the Lights and how to get the best out of your camera. If a tour goes out, and you don’t see the Lights, they will honor your ticket on another night. Reykjavik Excursions was the tour on which I saw the Lights for the 1st time (Feb 2016) and it was a better experience in the end than the private jeep tour we did on my second winter trip to Iceland (Nov 2016).
Definitely do NOT do the boat cruise for the Lights. Too crowded, hard to set up for pictures.
Final word about the Aurora: You may have to go out every night to catch them, depending on the weather, and if it is very cloudy or rainy, the tours might not go out. If seeing them is the reason for your trip, don’t wait til the last night. Start going out right away, and enjoy the chase. It’s a bit wild. Your driver will be heading out in one direction and then get a report that it looks good somewhere else, and off you go.
If you want to photograph the Lights, I’ve found two articles with good equipment lists and tips. In addition to the recommended wide angle lens, tripod and flashlight, you’ll want a remote shutter release and fingerless gloves. I like the kind with the mitten covers so your fingers stay warm when you are waiting around for things to happen.
Dress in layers: thermal underwear and good ski pants on the bottom, and thermals, a turtleneck, fleece and a good ski jacket on top. Warm hat. If you want a scarf, I recommend an infinity scarf so it doesn’t get in the way or get lost.
More Iceland travel tips: Iceland in Winter vs Iceland in Summer