Shoot all images in the best quality, high resolution and keep them full size; web designer will optimize and correctly size photos.
All photos should be horizontal in orientation.
Most photos must be wide and narrow - website photos span to reach the largest monitor and resize smaller. Think banner style when setting up the composition / shoot.
Shoot a variety of close-ups and distance to best provide the site designer with material that will work well for all pages/applications.
Shoot a series with a consistent area of white space, or copy space (blurred background), in mind. Many website designs have textual or navigation elements over the images.
The ideal focal point for home page images tends to be about at the ⅓ point - either right or left.
Plan some images where the focal point is centered
Know that your far right and far left edges of the image will often not be seen on smaller size screens
If shooting for a school, plan a series of shoots with students in school colors (spirit wear shirts, athletic/team wear, uniforms, etc.). The rest of the photos the subjects should be in neutral colors. Avoid clothing with graphics (other than school mascot/athletic wear).
If shooting for a school, shoot in a variety of locations that includes some of the classrooms and other environments to provide site visitors with a feeling of being on campus.
Background environment / location may be important. Be sure to obtain the subject's emotions but shoot a series that provides insight into what your location looks like.
Don't disregard "candid" photos - they can often be edited to work well for inside pages and galleries, etc. Review the overall quality and size; any image that is in a 300 dpi format is likely a good enough quality to work with on your website.
Focus photography shoots and resources on your home page. You'll likely obtain enough great shots to use for any landing pages or inside page needs.
Create a list for your photographer that includes the settings, age/people groups, etc. that you want reflected on your website.