I believe that a Discus aquarium should be entirely geared toward keeping Discus fish, as other species generally do not require the dedication and environment that Discus need. The setup, plants and other inhabitants should be carefully chosen for optimal conditions, giving the Discus fish first priority. Discus are calm, timid fish who like to be kept in small groups of five to eight fish, as like other schooling fish they need the security of a school around them. This also helps in reducing stress of acclimating to their new environment. Outside of other Discus, what tank mates you choose again entirely depends on the purpose.
If you want a nice display tank, Discus fish feel comfortable with small schooling fish such as characins. When Discus fish see the characins in the open, they are likely to come out sensing that they are safe to swim. I would recommend a large school of characins like Neon Tetras, Cardinal Tetra and Rummy Nose Tetras. It emulates their natural environment and both flourish in the same water conditions. However, you can keep most peaceful slow moving South American fish and Dwarf Cichlids with Discus, so long as they don’t dominate or out compete for food and space. Many have had Dwarf Gouramis as well as Pearl Gouramis with Discus, though I would not recommend the larger more aggressive Blue and Golden Gouramis. Smaller peaceful catfish such as the Corydoras will get along well with Discus fish and do a great job as bottom feeders.
As much as I adore freshwater Angelfish, I also would not recommended keeping them with Discus as they can grow large and bully the Discus, outcompete the Discus for food and carry diseases that Discus are particularly prone to catching. It can be done, but usually requires a much larger aquarium and a skilled aquarist. I’ve also known people that have kept Kribensis with Discus, but much like freshwater Angelfish I would not recommend that right away. One of my favorite fish is the Blue Ram (German Blue Ram, Ram Cichlid), a beautiful dwarf cichlid that will complement your Discus quite well.
For a breeding tank, only Discus should be kept and I would strongly recommend against adding anything else. While many love having Plecostomus and other algae eaters, they are notorious for latching onto Discus fish and sucking on their mucus covering, leaving the Discus vulnerable to stress and decease. That is not to say that the two have not been successfully kept together, but in my personal experience it has been nothing but issues. For a new Discus breeder it is best not to take unneeded risks, even more so with a fish as fragile as the Discus fish.
For more information visit this Discus fish guide.