Dress in layers and wear comfortable shoes.
When an Icelander tells you the weather changes every five minutes, take her seriously. In just one day, we went from wearing plain cotton t-shirts to pullovers to down jackets.
Most tourists start their day with the Golden Circle and end at the Kerid Crater Lake. So we did (and recommend) just the opposite - start with the Kerid Crater Lake in the a.m. There were only a few cars besides ours (and no buses) when we went.
If you or your kids aren't used to harsh winters, I would recommend going in the summer months to make the experience enjoyable for everybody.
Iceland is expensive and deals and promotions are hard to come by. I'd recommend getting an international no-fee travel card that gives you miles for using it. Most places in Iceland accept cards.