I have some extruded text that I want to rotate around like an old screensaver. The problem I'm having is that I can't seem to make keyframes do anything. I change the mesh position at 1:00f and put a key and then 0:01f is changed. I'm probably missing something obvious, all my previous animation experience is frame by frame.
From your screenshot it looks like you are key-framing the wrong item.
To move the model around you need to key-frame the mesh. Click on the arrow in the timeline where it says 3D meshes and expand it.
Switch on the key-frame (clock symbol) for your mesh. Move the model to add a key-frame, advance the time line and move the model again to a second key-frame ....etc.
Save before running (this should not be necessary but sometimes when keyframing multiple objects I do this to check the keyframes have all taken.