Decide what you want to get out of the trip- Northern Lights are fascinating but that usually means visiting Iceland in the winter. Going in winter on the other hand may limit some glacier adventures- glacier hike is more challenging and glacier lagoon is closed.
Compare prices, miles earned, and extra charges between low budget WOW airlines and Icelandair for the dates of your travel. Icelandair may be more expensive at times, but if you are collecting Alaska airlines miles, you will get some miles. Furthermore, WOW baggage fees can be very high.
If you plan to drive, reserve a car ahead of time. We used PROCAR Car Rental and their representative picked us up from the airport and took us to the lot. We opted for all possible insurance they offered, based on numerous trip advisors reviews (super CDW, sand storm insurance, etc.). Total cost of one week car rental in August, with all the insurance, was app. $1,300. If you decide to rent a camper and save on the hotel cost, a week rental with insurance costs app. $1,800. It is a cheaper option, but less comfortable.
For U.S. drivers no international driver's license is necessary, you can rent the car with your regular license only.
Reserve hotel ahead of time, at least for the first few days. If you plan to go to Blue Lagoon first, find an apartment that has a washer/dryer so that you can dry your swimsuits.
Weather/season permitting book the Glacier Walk and Glacier Lagoon tours ahead of time. They go fast. The glacier lagoon tour is only open May to October.
Pack waterproof/warm clothes, hiking shoes/boots, warm hiking socks, etc. Most of these items you can buy in REI (being dry is worth every penny). They carry plus size as well.
Chances are it will rain a lot. Forget about the umbrella and focus on waterproof jacket. You will also need a rain cover for your backpack.
Pack swimsuits and hair conditioner (many hotels have shampoos but not conditioner). If you are going to volcanoes in Myvatn region, bring a fly net- you will need it. The annoying flies aim for your nose and eyes as you climb up.
Dress in layers. Dress in layers. Dress in layers. Did I mention to dress in layers?
Iceland is very expensive and most of Reykjavik hotels do not offer free breakfast. If possible pack food (ramen noodles, instant oatmeal, energy bars, peanut butter, etc.).
If you are on the road, buy food in supermarkets and make sandwiches for the next day.
No need to bring lots of cash, they accept credit cards almost everywhere. Even in the bathroom stalls.
The water in Reykjavik slightly smells of sulfur but it's not horrible. It's nothing compared to Myvatn in the north.
Pay attention when driving, the signs on the road are very small and inconspicuous. The bridges are often one-lane bridges, so adjust and watch the road ahead before deciding to cross the bridge. Most bridges are short enough so that you clearly see if there is incoming traffic competing for the same lane.