For a 16" f4.7, assuming visual use only, an 18" tube ID and a 1.6" focuser, I would use a 2.6" secondary. If your tube is wider or focuser taller, you may need to go up to a 3.1". For planetary only use, you could go down to 2.14"
For a 12" f5.8, visual only, 14" ID, 1.6" focuser, I'd use a 2.14" secondary, although you could get away with a 1.83" if you want primarily planetary use. Again, a wider tube or taller focuser may make you bump it up to 2.6".
For photography, you would need to go up a few sizes for both, depending on how wide you want your non-vignetted field to be.
To play with the numbers yourself, download Newt 2.0 from: http://home.att.net/~dale.keller/atm/newtonians/newtsoft/newtsoft.htm