Mapping signal dynamic range
I've used these two circuits in several different applications:







simulate this circuit &ndash; Schematic created using CircuitLab

Inverting with variable input impedance dependent on Gain.  No interaction between Gain and Offset.







simulate this circuit

Non-inverting with high input impedance.  Gain is slightly dependent on the Offset setting.

This doesn't answer the entire question - I'm leaving some engineering work for you to do - but it should get you started.