engraving steel sheets with a punch set - what can go wrong?
whether a normal (500g?) metal hammer or rubber mallet will do


A 500g/1lb metal hammer should be fine. A 1000g/2lb would not be overkill


whether I will need any kind of support (e.g. special bench) or if I
can improvise one easily - I assume I need a hard material


Solid support is needed, but it need not be hard. End-grain wood is typical - a straight section of log/firewood will serve. Set on ground or a concrete floor to minimize bounce, or use a very heavy support.


whether the steel sheets are appropriate for engraving - not too hard
for the punch set?


Stainless steel in most grades is very difficult to punch as compared to mild steel. You should also realize that you are not "engraving" which is a cutting process (can be done with cutting tools or acid or electricity, but material is always removed) - you are stamping (or embossing) into the face of the material, deforming it to make an impression. In stainless steel, that deformation causes "work hardening" so it can be quite difficult and may exceed the capacity of your punch set. Using a thinner stainless sheet in "dead-soft" condition as sold might help with that.

A simple wax-resist chemical or electro-chemical engraving process might be a lot easier (coat with wax, scratch through the wax to the bare metal, immerse in an etchant bath where the bare metal is eaten away and the metal protected by wax is not.) 


Anything else I should know or haven't planned for?


Wear safety glasses for sure (the potential to have a chip fly off the hammer or punch and into your eye is always there) and hearing protection of some sort is also wise when hammering.