In most cases for vector file requirements a .AI or .EPS file would be the most preferred file type. However if they request a rastorized image but still want layer abilities a .PSD, PhotoShop file as long as the requester has PhotoShop is your best bet!
In order to save on file size, combine the main layers together and then ZIP the file as well and this will reduce the file since some PSD files can get rather large. If its too large for email you may want to consider a file upload site like
http://www.mediafire.com/ to share the file.
Best of Luck!