We (three of my friends and I) rent their category C camper for our road trip around Iceland and it was probaby the best idea we ever had. Literally became our home. We were never cold, never wet, and it was quite nice to be able to make some tea right after a nice hike in a lovely unpredictable weather. We had the freedom to explore Iceland without restrains other than the unpaved roads. The camper was really well equiped, clean, and the beds were quite confortable as well. We drove the ring road in 10 days, and it was enough (even though the more you see, the more you want to see)
The kukucampers staff are also incredibly nice human beings, really helpful, and it made the whole experience ever more perfect.
As for the parking: in the west and the north, we were lucky. We were in Iceland in the end of may, slightly before the touristic season. We found places were there were no indications that you can not park overnight and we didn't have problems. We left the places as we found them (that means no garbage of all sorts, not even toilet paper. Seems obvious for some people, but is obviously not for some others...) In the south and east, there were more people, and less places to park, so we went to camping sites. Some of them were closed but you were still allowed to camp there (but no toilets, no showers most of the times). Still, camping sites are great. Some of them have wifi and a kitchen, and having a proper shower is quite nice too, don't underestimate it. We paid between 1000 and 1500 ISK per person.