Basically you are talking about getting an existing link changed so it now points to your site instead of where it currently points - whether any cash changes hands or not. The situation can be as simple as "don't you think my website offer your visitors a better resource?"
In recent times, I've become convinced that too much matching of anchor text across backlinks really can cause trouble. Google will register ANY change and run it through their backlink algo, which seems to undergoing some evolution or mutation, and probably will continue to - well into the future.
So as long as the page is on-theme and the link is not in some suspicious looking page position, I'd be content with even a "click here". "Website name" would be good, and as long as it's not overdone throughout your backlink profile, some keyword anchor text is very helpful.