I'm building a newsletter in InDesign and have some company photos of people's faces. What file type should I use to place them in my InDesign file?
It doesn't really matter too much, providing your effective pixels exceed your desired output. If you want it for printing at 300ppi, as long as the image isn't stretched beyond that, you will be fine. In the end, InDesign has to resize/reinterpret your image anyway to match your output settings.
You can monitor the effective pixels in the info section at the bottom of the links panel.
If it's a printed newsletter, .tif or flattened psd. Using EPS doesn't allow you to display some extra info in the link panel of InDesign (resolution, color mode, etc.). JPG can work too but it's risky that you will allow for compression when you save the image (if you edit them).
If it's an emailed newsletter, you shouldn't be sending a big image in one chunk in an email so I'm guessing you have a Web integrator working on this. The Web integrator should optimize the images to jpg, gif or png to put in the newsletter after you are done with the design. So what you work in doesn't really matter in this case.
EDIT (hadn't seen your comment concerning output): Since your newsletter is going on a Web site, use what you prefer but try to avoid compression at first while designing and keep your original images in RGB as they will have better color (CMYK doesn't accomodate all the colors that RGB does). The final steps depend if you are considering coding the newsletter or if it will be output as a single image.