You say you don't know how much you should pay "for clicks". But, in your original question, you say you are thinking of running an affiliate system. Usually, in an affiliate setup, you don't pay per click. You pay for results. You typically pay a percentage of the value of each sale. Since you are not selling anything, that doesn't really apply.
If you really just want to pay for visitors to come to your site - regardless of what they do when they get there - you should consider setting up an AdWords campaign. You would have to decide which keywords you want to target. The system will then suggest the amount per click that you should pay. The great thing about that system is that you can measure the results, and fine tune the amount up or down accordingly. Or, you could start with a very low amount, and gradually increase it until you have hit the level that brings in the desired number of visitors.
But I still question why you want to do this. You will be spending money, but I can't see what you will get in return.