A patina is a lovely thing. If you polish, try keeping it superficial. Just shining up the most pronounced features in the engraving and leaving the crevices dull gives a wonderful effect.
I have a collection of antique copper. When I first buy an object it will often have the crevices filled up with leftover polishing abrasives. This is not what you want. When using an abrasive go with the RED mentioned above (red of Paris). This is a tried and true method for polishing with an abrasive agent.
The buffing wheel is also a great suggestion. You can buy a small buffing tool yourself and start with the softest of the buffing wheels (often included in a small set, you'll find it for cheap in a big box store).
If you do choose a polish, try an antique polish with a very small grit or without an abrasive suspended in it. You want one that smells like paint thinner, not one that smells like amonia.
Vinegar is quick, available and cheap. The acid will however etch the metal and will not produce the shiniest of results, especially when left on long.
Lemon and salt are very effective but way too aggressive for fine engravings.
For any method (except acid methods), make sure to let active compounds evaporate and then give the surface a thorough wash. For all methods take apart mod first to avoid things getting in grooves or between moving parts.