For this road trip, the best way to get around is by renting a car. The Ring Road, which circles the entire country, is paved and easily accessible for most of the year. Be sure to check local weather conditions and road closures before driving each day. Gas stations are common along the Ring Road, but it's best to fill up whenever you have the chance as some stretches of the road can be remote. Car rental costs vary depending on the type of car and time of year, but expect to pay around $50-100 per day.
If you have more time, consider adding a day to explore the Westfjords or take a detour to the remote Askja Caldera. If you have less time, consider skipping the Egilsstadir and Akureyri stops and heading straight from Vik to the Snaefellsnes Peninsula.