Blue Car Rental is right at Keflavík Airport, so you can pick up your car immediately after landing.

In case you are driving around Iceland in summer, you really only need a 4x4 by when you go into the highlands (on the F-roads). Other than that, you will be fine with a regular 2x2 car.

In winter you actually also don't really need a 4x4, but I personally feel more comfortable in one when there is a lot of snow or ice. So I would recommend taking a 4x4 that time of year. But if you are used to snow and feel fine in a regular car, that is fine as well. And in winter, all cars in Iceland (both regular and 4x4) have spikes in their tires, so you will have a lot more grip on the road when it is icy.