I haven't been in this position, but I would worry more about making such an announcement prior to publication. Most journals simply don't want old news (i.e. news that already exists in the public domain). This is a tricky subject.
Tricky indeed, because you also run the risk that the public does not take you serious when you have no back-up in the form of a high-impact factor journal; you may have invented the whole show.
discover->submit for publication->when accepted, work with publication about media->if you want, schedule a talk at a meeting that coincides nearly with publication date->press release comes out on the date of your talk
Great answers. Another quick point: most journals offer avenues for rapid publications of important results, so there's always an option of having discoveries vetted by peer scientists prior to formal announcement.
The only reason I think I would call the media before publication is if I have run out of money for the field work or the preparation of the specimens and I need to find private sponsors or the backing of local authorities in order to keep working.
Many thanks to all for your thoughtful answers. Is the situation different if the reporter calls you? I have a telephone appointment with a print reporter in 45 minutes.
The interview went very well. I did provide some specifics but I don't think that anything will appear in print until during or just prior to the meeting. The reporter plans to speak to other scientists, so I anticipate something resembling an "in public" peer review. Sir Peter Medawar said that secretiveness is a disfigurement in a scientist, so perhaps this is for the best . . .