I think allemansrätten says you can camp out basically anywhere you want except within earshot/line of sight of houses. Need permission to light fires or stay more than one night AFAIK. No littering of course and you should probably limit your shits to cat holes.
Water is less of an issue up north as fjällbäckar are pretty safe.
SAS has youth tickets that are pretty cheap if you're under 26. Looks like you have to join some faggy club to take advantage of them now though.
http://www.sas.se/?cep=236433&wt.ac=start_boka-ungdom&wt.seg_4=start_boka-ungdom.
Sometimes they're cheaper than the train. If you wanna try Norrland I mean. Don't have to go much farther than Dalarna for some Norrlandskänsla but getting around without a bike or car might be problematic.
Don't bet on mushrooms unless it's foolproof, like cantarelles.
I live in Nynäshamn and we have some real nice unexploited archipelago down here but of course natural drinkingwater will be an issue here as I imagine it will anywhere this side of Mora. I might recommend somewhere west of Nynäs. Not sure if Lisö is too inhabited, slightly SW of Stora Vika and an hour or three from Nynäs proper on a bike. Failing that, there's the immediate area around Djursnäs which is very nice and idyllic, or Järflotta which is in large parts some kind of naturreservat. The boon with living near the sea (within hundreds of meters) is stabler temperatures, the downside being wind.
https://www.google.se/maps/dir/58.9041262,17.9459375/58.9266843,17.8234172/@58.9106116,17.8679962,5647m/data=!3m1!1e3!4m4!4m3!1m0!1m0!3e0?hl=svFuck it, I might even volunteer my shower and an occasional hot meal since you're probably shit out of luck trapping let alone hunting (poaching, let's face it) anything here. And I've never known the fish to bite very well either.
Pic is taken near Evagraven/Fiskhålsgraven in Härjedalen.
