Hi there,
Don’t picture jam-packed highways—everything’s relative in Iceland! Route 1, which you could call the main road, stays pretty quiet.
A 4x4 camper van is definitely a great compromise if you can afford it. Otherwise, for a first trip and a taste that’ll make you want to come back, a regular camper van can work just fine. Lots of "secondary" roads are now paved, or unpaved but still drivable. Most tourists stick to Route 1, but with a little curiosity, you can easily reach spots that are way less crowded than the big tourist sites.
I’m thinking especially of Route 910, with its "highlands" vibe and the stunning view of Vatnajökull on the horizon, leading to the little Laugafell hut and its hot spring beneath Snæfell (a small peak in the southeast—don’t mix it up with the one on the western peninsula). For us, it was a magical memory, and no 4x4 needed.
This was six years ago, so I hope things haven’t changed too much! I also agree that you’ve got to adapt to the weather and not insist on visiting a region where bad weather’s forecast for a whole week when you’re only there for 10 days.
Happy exploring in Iceland! !