What networks would be a good starting point to look at? Who are the reputable and established players in this space?
At first glance, Google AdSense does not seem to have the level of control I am looking for.
There are also companies that work with multiple networks (like Adsense, and others). They usually charge a fee or take a cut of your revenue. Google calls them publishing partners. Their list can be found here: https://www.google.com/ads/publisher/partners.
After this investigation, I went back and had a second look at AdSense. In my initial quick look around, I missed the manual ad configuration mode. In this mode you can pick from four different ad types. After including the AdSense script, you add the AdSense HTML snippet where you want an ad to run then invoke a line of JavaScript which causes the ad to be populated.