How can I use gate/sensor dimensions and field of view (is "field of view" the same thing as "focal length"?) to adjust the way my camera shots warp? I desire a wide angle without some of the weird perspective warping.
There's nothing weird about the perspective warping. The blender camera behaves just like a real life camera. From the camera presets you can even choose some common cameras, but you can set the blender camera to mimic any camera. Just look up the sensor size of any real world camera and enter those values for the blender camera. In addition, if you'd want to match a particular shot, you could look up the meta data of the picture to see what focal length and which f-stop was used for the shot and enter those values too.
You're going for a wide angle, which means a focal length of about 20mm which translates to a filed of view of about 60º. Any distortion resulting from this setting is perfectly normal for such a camera. However, if you want to adjust the distortion, then - depending on what you're going for - you can use the shift property in the camera settings, or you can use the Lens Distortion node in compositing to manipulate lens distortion.