Svenn- you can make a cheese board as "meal-like" as you want for as many persons as you want depending on 1) number of cheeses, 2) charcuterie 3) fruits/veg 4) bread and wherever else you want to go. Don't count out soup as an option as well.
Simple, can be easily paired with. And yes, sparkling wines, red and white can work and are the preferred choice with some cheeses (for example, moscato with certain blues). I've planned dinner for 20 that was all cheese courses and charcuterie.
Here are a couple of simple suggestions:
Bread: if you are serving just one cheese, a little brie or whatever, just stick with a good fresh baguette, warmed. If you add a few other things, more cheese etc, add a nice raisin/raisin nut bread.
Fruits (fresh): really easy and good with ripened cheese: green apple.
Fruits (dried) dried figs or medjool dates.
Nuts: for a small board, keep it very simple; one kind, just a few. marcona almonds are the stereotypical choice. Fresh walnuts are nice.
Meats: just my preference, but I don't pair French ripened cheeses with cured meats; IMO they overpower the mild flavors.
Wine pairing: buttery/creamy/triple-cream/brie etc hold up well against tart/acidic/tannic wines and can shine... again, a blanket generalization... all depends on what's on the plate.
All that said, since you mentioned champagne and a preference for strong flavors, here are a few easy combos you'll often recommended with cheeses that will be easy to find:
Small Plate - One Cheese
Cheese: Pierre-Robert, Epoisses or Reblochon
Accompaniment: baguette, green apple or strawberries
Add two cheeses
1) Add a fresh, plain goats milk cheese ( I like Wabash Cannonball)
2) Either Aged cheddar - Montgomery (English) is the classic example -OR- Manchego/Mahon... a harder cheese for texture and contrast
Need more? Add a little quince paste or a fig spread/jam. Perhaps add that dark bread, like raisin or a brown bread (plain)