I may hesitate to call an Irish Coffee a cocktail (it’s typically listed under hot drinks in a menu), but in any case, the coffee from your setup is pretty much exactly what reflects the preparation method that would have been prevalent in Ireland back in the 1940s. Another option that would also fit the time window would be a percolator, or a vacuum coffee maker (siphon).
The strength is up to you, usually people would aim for a slightly stronger brew as sugar, whisky and cream will be a strong counter-part, in a gustatory sense.
Modern preparations may use an espresso machine and draw a lungo, simply because it may be the setup available in many bar or restaurant settings. There is no reason though to invest in one just to make an authentic Irish Coffee (you wouldn’t).
In a more general sense, there is no one-fits-all coffee preparation for cocktails. An espresso martini would obviously call for an espresso, but there are countless recipes out there that use pretty much any kind of coffee. Usually the recipe should specify which kind.