All DVC Units will a Mr Coffee style brewer (basket/flat bottom filter). Most villas have a full size (12 cup) brewer, but some studios have a smaller 4 cup brewer. If you are in a studio and it has the 4-cup, you can call housekeeping and they will bring a full size brewer on request.
The 12 cup machines do come with one or two pre-packed filters - just pop in the basket - but they also accommodate the regular flat bottom filters and your own coffee.
Sometimes you might get a pod coffeemaker for those DVC resorts attached to a Disney cash resort. The cash resorts use the pod coffeemakers and housekeeping will sometime replace a broken coffeemaker with a pod one in error.
Joffrey's Coffee & Tea Co. has the new coffee contract with Disney and I think that the resorts are getting portion packs for use in the Mr. Coffee machines.