We went to Landmannalauger this September, an amazing place. The Laugavegur trail is far and away the most popular trail there but having said that, it’s not Langdale on a Bank Holiday. There were maybe thirty cars around the campsite and car park plus people that had come in by bus.
There were a good few groups setting off on the Laugavegur but looking along the trail (we went up one of the nearby mountains) they were well spread out so to all intents each group was on its own.
Tent pegs are all but useless on the campsite at Landmannalauger, it’s basically solid rock that you are camping on. A tent that is capable of being free-standing like a dome will be useful and wrap the guylines round rocks. I imagine most of the other sites will be similar.
Clothing wise: think Scotland in winter. I.e. you don’t want ultra lightweight kit, it just isn’t going to stand up to the wind. I had a MT500 jacket which was about right. Plenty of warm clothing especially if you are going to be hanging around camping rather than in a hut. A decent inflatable sleeping mat – see comment above about ground – and a three season sleeping bag. Not sure if there are any river crossings on the Laugavegur but it might be worth taking Crocs or similar for them and keep your walking boots dry.