My exp of wildcamping in Switzerland: people seem to turn a blind eye provided that you only stay one night in one place, pitch up late and leave early. Have been several times with my bf and we're planning on doing so again soon. You can find some nice spots with a fountain or source nearby, good view, wood for fire etc. Camped in various cantons including Neuchatel and never had any problems, just one time we picked somewhere which wasn't an ideal spot.

Not sure about campsite prices but bear in mind you potentially have no view, noisy neighbours, and can't make a fire... For the tents we bought ours in England so no advice there.

Enjoy!