There are many things to consider.
It is not really important whether it is copper or not. (Copper is for tourists in Turkey and generally of bad quality.)
- I advise you to choose a stainless steel one. If you choose copper, find a real thick copper one.
Here, you can see a very good, thick copper cezve that I encountered. However, this is quite expensive (>100$) and really hard to find even in Turkey.
- The thermal capacity... The thermal capacity must be high. It's hard to explain this on text. The cezve must be a bit sturdy. This is all I can say. The copper ones aren't generally sturdy. A bit thicker stainless steel ones are nicer for that. So, you can brew your coffee fast and also homogeneously distribute the heat. This is quite important when preparing your coffee in your own hands. The traditional copper ones are traditional as copper was easier to produce historically. Steel is easier to shape now. So, you can go for steel. An indicator for good thermal capacity is the boiling character of your coffee. If your coffee starts to boil from the edges, then it is possible that the thermal capacity is less than it should be (or the fire is way too strong to brew coffee).
- The bottom must be a bit larger than the top. So you can easily keep it on the oven.
- The slope I can advice is abut 10 degrees from bottom to top for best brewing.
- The height must not be more than 10-15 centimeters to stir the coffee easily.
- Take care about right/left-handedness. Some cezves have the option to flow the coffee only on one side.
I hope this will help.
Here, I'm adding a photo of my own. It is a right-handed stainless steel one. It's thickness is about 1 mm. No slope at all.
