The above question is a complex one right now because we are spoilt for choice. Ordering coffee in Suisse Romande is quite different from that in France simply because in Switzerland the Italian origins of a good coffee are much appreciated and therefore the words of Italian origin are not frowned upon.
If you like your coffee strong then you obviously like the Italian “espresso”. In French the Italian word can be abbreviated to “un espress” or for your sake: anespres. And then of course, silvu:ple.
If you like your coffee less bitter and a slightly larger volume, then “un café” is the correct term to use.
Unlike in France you are allowed to order “ un cappuccino” in Geneva. FYI: in France the correct term would be “un café crème”.
A “Swiss coffee” would be to ask for a “renversé”, that is: coffee with steamed milk. What is the difference between a cappuccino and a renversé? Well, the quantities for one, renversé is as big as “un café”, and second: the order of the ingredients. With the renversé the steamed milk gets into the cup first which is subsequently followed by the coffee.
Obviously, with the advent of Starbucks, the selection of types of coffees has quadrupled, but if you prefer traditional coffee places, then the above ones are very likely to be part of the menu. Enjoy!