What kind of institution can apply J visa for F1 student? Only university? How about company or public school system?
-All you mentioned are possible J1 sponsors. To be a J1 sponsor,the public and private entities have to be designated by the Department of State (DOS). So, just ask your postential employers whether they can act as exchange sponsors (J1 sponsors) and they will tell you about that. For more information, see this DOS website:
http://exchanges.state.gov/about/program_offices.html
I know H1B is better. However, it is a kind of suffering for me to study at school. If offer comes, I would like to start early using J
