Answer :
ermm i mean a journal reviewed by peers you mean by other professionals working into that field? Everything else seems to be correct i would do a little more research on that.
The discovery should be first published in a journal to be reviewed by other scientists to ensure that it is correct/repeatable. After this, the discovery would most probably be reported in scientific magazines and then in newspapers, important discoveries would probably be reported by newspaper quickly though which leaves the potential for a discovery to be untested and incorrect.