Take a look at where Iceland is on a map, its latitude is similar to that of southern Greenland, Sweden, and Alaska. Go much further north and conditions are uninhabitable.
The Ring Road, also known as Þjóðvegur 1 and Route 1, is an 828-mile road that runs around the circumference of the island.
Our recommendation would be to take your time in Iceland as there are so many amazing things to see and do. At least one week, preferably two, would be the ideal duration.
Iceland is known as being an incredibly expensive country and it would be a difficult place to travel on a tight budget.
Getting from Keflavik Airport to Reykjavik can be an expensive affair with a taxi setting you back $100-120. A more affordable option is the Flybus but even that will cost you ~$25 per person.
While it’s possible to see Iceland as part of a tour group, if you want the freedom to explore the country at your own pace you should definitely rent a car.