Which rear cog should I remove if I want to add a 26 for climbing?
The answer in terms of ratios might not be the same as the answer in terms of being able to shift. Taking out the 16 would be reasonable but then the shift ramps and pickup teeth wouldn't align. This issue will occur going from the 23 to the 26 whatever you remove. 

You've got 8 gears in the back so I assume you've got indexed shifting. If you're using friction shifters it's not an issue as you can overshift then back it off.

Further reading from Sheldon Brown