Tool to count clicks (for PPC) properly?

I have an affiliate website with product recommendations where online stores often contact me to advertise. The way the website is made up the best offer is to let them be a part of the product recommendations and pay per click (PPC). A monthly fee to be a part of my database is not a viable option as the amount of visibility could be difficult to handle and some may not get too many clicks.

Now, my problem is that I don't really know how to count the clicks in a reliable, bot-filtered way. I.e. a way that I can feel confident in invoicing my customers according to the data. Currently, I am counting each click on each link but it does not know if it is a bot or not. I don't feel I can, or want, to program my own system for this but rather rely on an external service for it. What options do I have? Preferrably free.

I know I can use Google Analytics events for it but I haven't really been able to make it work properly (I am not too familiar with javascript). I would assume there would be simple options for this that act as a pseudo-affiliate network but I can't find any. Any tips?