you already have illustrator so you are good to go this is a vector based program.
designing in illustrator means using original images, text, shapes.
Importing bitmaps, jpegs and pngs does not make the entire image/file vector. You can import these types and live trace them to make the entire image/file vector and save as an (ai.) most printers prefer (.eps)
Now if your imported image is poor and will not trace correctly and you prefer to keep it and then add some original images or text then save as an (ai.) or (.eps) ONLY the original image and text is vector and the import images (bitmaps, jpegs and pngs) will remain that and the quality could be poor depending on the dpi and clearity of the image
So just because you save an image/file as an (ai.) or (.eps) does not always make it vector. So if a printer kicks it back to you and says its not vector more then likely it was an imported image that you did not live trace.
Also, illustrator live trace isn't always the greatest so you can use vector magic (there is a great explanation on what is exactly vector images) we purchase the 3 months at time version and you get credits towards the desktop version.