depends on the type of ink or pigment you use. most any surface should work if the engraving is suitable for printing. way, way back, all prints were made with wood, then i think copper came into use. other metals as well. copper is very easy to cut, as you know, but in any size will be pricey. you can work with relatively thin ga copper, but for printing, it must be affixed to an absolutely flat surface. have fun.
I'm an old stationary engraver from way back. I used to proof engraved plates and dies for an engraved stationary house. The press I used was a D type hand plate press. Basically I would put the plate on the movable bed, ink it up, wipe off the excess ink. Leaving enough in the engraving. Place a dampened piece of soft card stock on it and squeeze the whole thing through the round part of the D by turning the attached spokes. Walla a printed proof of an engraved plate.
Cronite Co. still supplies this field of engraving. I would suggest engraving on steel plates they supply for the purpose. Much cheeper than copper and made for engraving.
What size of prints? If it business card size, Jim's advice is right on the target. For the printing you can find all steps on i-net. However if it bigger size, rolling press has to be used. It is expensive, but some Art colleges have it, look around in your area.
As for the metal, copper, zinc, soft steel are OK. Copper is the best, it holds a chisel without slippery, providing very flexible line, zinc is the same, but softer, steel is good for large editions and finest lines. So, try!
It is etching, not engraving, but printing technique is the same.
size 6X4