My van was a "Happy 2 Ex" from Happy Campers (http://www.happycampers.is/
) It was very basic - I think they convert the vans themselves. The "Ex" means it was one of their older mares just about to be put out to pasture - it was cheaper than their newer ones. I had reserved a Happy Ex 1, but oddly the people that arrived 5 minutes before me chose to downgrade from their reserved 2 to the 1, so I got their 2 for the price of the van I had reserved (got a bigger van).
It had a fold-down double bed / back seat, ARB 12v cooler/fridge, a Wabasto diesel furnace, and a sink with water pump. It was most definitely not a 4x4 and is prohibited from the interior F-roads (the police will fine you if they catch you on those roads anyway). They provide a butane one-burner stove and some basic dishes / utensils.
The bedding they provided was rather pathetic considering how cold it got (below freezing and my heater decided to crap out on me - but at the price of fuel there, that may have been a blessing!). I ended up buying a cheap sleeping bag to supplement their thin blanket after one night being cold. If I go again I will take my own sleeping rig.
It was by no means posh, but it did the trick and let me get out of the miserable weather I had. There is something to be said for simplicity, and I found myself kinda liking the minimalist setup.
There are other more involved and more expensive camper options - up to pretty large rigs as well as 4x4s. I was alone, and don't require much so I was content to keep the cost to only one arm and one leg. I'm still walking funny from the unkind intrusion to my nether regions by the oil companies and the amount of cash I spent on diesel (~$2.25 / liter). I really wish I could ship the SMB over there, but feeding the gluttonous hog would be really painful there!!!!
The good part of the campervan is that for now you can park and overnight pretty much anywhere in the country without getting harassed by officials. The locals are starting to get grumpy, though, and are starting to limit the freedom camping. I parked on beaches, info pullouts, picnic pullouts, and a couple road closure gates with no one caring enough to bother me (not sure anyone even went by at all in most of the places - there aren't that many people in Iceland). Regardless, with trying to photograph late into the night for the sunset (around 11:30pm and later), having the van made it easier than trying to sneak quietly into a farmhouse B&B at weird hours. There are a lot of community pools in Iceland towns/villages where you can take a shower for a couple bucks.
For my purposes the campervan option was the ideal way to go - my entire rental was ~$1300 for 11 days, though I snuck in at the very end of the off-season rates; summer rates are higher. With no other lodging cost it was about as cheap as I could do this trip in Iceland for vehicle and lodging.