How would I cut out lettering from a stamped piece of thick-sheet metal
A jewelers saw (also known as a piecing saw) should do the job these have very thin, fine toothed blades, almost a like a flattened wire which can handle very intricate cutting jobs. 



Image from micromark.com

You may also want some needle files to tidy up the cut edges afterwards. 

You will need to drill a small hole where you want to start the cut. Then you can disconnect one end of the saw blade from the frame, thread it through the hole and reattach it. 

These saws to take a bit of skill to use effectively but if you get the basic technique right you can achieve good results with care and patience even if you don't have much experience. The big advantage over power tools for something like this is that you have a lot more control over the rate at which you cut so there is less chance of making mistakes. It is also important to use the correct blades for the job, which is largely determined by the thickness of the material. If you use too coarse a blade for the thickness of the material it will tend to snag and jam. For metal around 1.5mm thick you are looking at around 50 teeth per inch. 

Similarly you need to set the correct blade tension (do this by flexing the frame of the saw against the bench as you attach the blade), it should give a clear 'ping' when you pluck it like a guitar string. 

Also bear in mind that the teeth are directional and conventionally you should be cutting on the pull stroke (downwards if you are using a bench peg) this means that the work is pulled into the peg, keeping it stable and the blade is only loaded in tension.