In my opinion cheese should be served before the dessert, that is the French way of doing it.
The challenge with serving cheese as part of a meal is actually the wine. Not always, but oftentimes. Usually the main course is some kind of meat with an accompanying red wine. Cheese in general pairs best with white wine. But serving a dry white after a red may represent some kind of a down turn. Therefore, when choosing your cheese you have to think about the wines when you select the cheeses to serve. You have to pair the cheese to the wine.
As part of a meal, do not overdo the cheese. A maximum of three different cheeses will do, and only a small piece of each. If you want to serve just one, that is OK, but make it a special one. Some garnish as well, such as marmalade of some sort, honey and a piece of bread. But make sure the garnish fits the wine as well.
Here’s some cheese recommendations to certain wines:
Port
To Port I would have served two different cheeses, and both British.
Stilton or rather the raw milk Stichelton.
Aged Cheddar, mature, farmstead and of raw milk. Which for all practical purposes mean West Country Farmhouse Cheddar from Keens or Montgomery or the Scottish Isle of Mull.
Stilton or Stichelton might well drown the Cheddar, so it is important the Cheddar is mature.
Moving on to the dessert I suggest serving something chocolate so you can just continue with the Port.
Sauternes
Roquefort, goes without saying. It’s a classic.
If you want more than the Roquefort, try a Livarot from Normandy.
Sauternes work well with a suitable dessert as well.
Red wine
If you have served an excellent and mature red wine with the main course and you want to continue with that, you may combine cheese from the list below. Combine soft, semi firm and firm, but not more than one of each.
Soft:
Brie
Camembert
Pont l’Evêque is a washed rind and way more pungent than Brie and Camembert
Semi firm:
Tomme d’Auvergne
Tomme Crayeuse
Bethmale chèvre
Firm:
Emmentaler
Salers
Mimolette
Tomme de Savoie
For the dessert it would be proper to change wine.