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pdf or eps
to color seperation offset printing
Tiffe
to plotor printing ( inndoor or out door printing )
The best solution is to call the printing house with which you want to cooperate and ask about the guidelines. By default, a PDF is sent (raster graphics should have 300dpi resolution for small printouts, the bigger sizes can have smaller resolition for example 150dpi - the size of vector graphics doesn't matter - but please remember that if the lines in the graphics are too thin, the printer don't prints them - I encorage to consultation with the printing house )
If you have any question, don't hesitate to contact me. Good luck :)
.PDF files are the best. Specially if they are editable in Adobe illustrator. Since they can be previewed on any device by any non-designer person