Peer review, a credible "publisher," and printed copies of the journal. Eventually, ISI or similar indexing/rating of the journal would also be needed. The third point does depend a bit on the field. In the humanities, the journal almost certainly must be an actual paper journal to be considered high quality, but in some of the hard sciences, computer science, etc., some of the e-journal articles get thousands of cites a year. Often, new journals entice important scholars to publish in their first few issues to raise the profile of the journal, and the editorial review board should contain excellent people to again raise the profile of the journal. Finally, I would add, that any journal that has a pay for publishing model will probably never be considered an excellent journal in most fields.
In the hard sciences, a journal can be purely electronic (i.e., online only) and have a good reputation. It also helps if the editorial board includes prominent experts in the field.
The editor and also the editorial board have to be internationally recognized experts in their field (it would be good to get good reviewers, too) and the first couple of issues should contain papers by well-known scholars; also, those papers should get cited soon. It will take a couple of years before the journal can apply for an ISI index; after that, a good journal should get a high index.
Among the points that have already been made, I agree on the following:
- A credible peer review system.
- A credible publisher, preferably well established in this business.
- Editors of good reputation, both in the specific research field and as previous editors of other journals.
- Capability of attracting first-rate authors, as demonstrated by at least the first few issues (the editors' job will be getting enough invited contributions of this type).
I would not consider publishing on any journal, new or old, that does not fulfill all the above criteria.
In addition, I would add to the criteria:
- No page charges, or at least a system that allows the publication free of page charges for authors who don't have publishing funds (in other words, acceptance of an MS should be based on the scientific value of the MS alone). If the journal has a paper version, there can be limitations for no-charge contributions, e.g. a maximum number of pages and illustrations.
I don't think that a paper edition of the journal is a necessary requirement, although it could help to distinguish between legitimate and predatory publishers (the latter tend to publish only e-journals). Many large university libraries, at least in Europe, prefer not to subscribe to paper journals and, if possible, only offer access to e-journals.