This concerns .ico format icons.
My thinking is:
16x16x8bpp (256 colors) - Legacy support.
32x32x8bpp (256 colors) - Legacy support.
16x16x32bpp (16M colors with alpha) - Natively supported on XP and up.
32x32x32bpp (16M colors with alpha) - Natively supported on XP and up.
48x48x32bpp (16M colors with alpha) - Natively supported on XP and up. Important for Windows Vista / Windows 7 desktop icons.
For the non-alpha channel images, if a lower color depth will properly accomodate the image, I will substitute a lower depth. For example, 16x16x4bpp (16 colors) might accomodate very simple logos.
(In particular I will omit the 256x256x32bpp for bandwidth concerns.)
Will most browsers of the IE7 era and up be able to work with this? Any other recommendations?
Yes, most browsers of the IE7 era and up will be able to work with that. Your thinking seems correct. Using the .ico format rather than the .png format is also more likely to work with any version of IE.