I´m afraid there is no getting round the cost, Iceland is just incredibly expensive. [redacted]
If you are planning on doing ANY off roading then you must get a 4WD. All 2WD vehicles are banned from using the F-Roads (off road tracks) and heavy fines await those that do.

However there is plenty to see if you stick to the main roads, so a 4WD is certainly not a must, it just depends on what you want to do.