In reply to cousin nick:
June is way better if you're concerned about mozzies and crowds. There will be more snow around, especially higher/sheltered places. (Some streams will have decent snow bridges for easy crossings but take care)
Kungsleden, as you probably know, is a very popular hut based trek. If you want a more solitary experience take a tent and do a lot of detours/passes. Highly recommended and way cheaper than using huts.
My favourite areas are
Down south, Hemavan area, super easy acces and pretty spectacular setting
Sarek and west Padjelanta( Sulitelma) can't go wrong really. Pretty wild in places.
Nikkaloukta-Abisko via Vistadalen-Nallo or Tarfala and the three passes.
I've spent a couple of months in the region but not more than a handful of days on Kungsleden. If you're fit enough to carry a big pack and knows some basic navigation I would recommend you to do the same. Even if you don't want to carry full camping kit, please look for some of the smaller huts outside Kungsleden as well.