Hi jmaster
I would suggest getting a 10 or 20 gallon tank to raise them and breed them in. If you can set up a 20 gallon just for them, they will reach maturity faster. You can clone a tank from your main tank for a fast cycle.
If they are still quite young, just set it up in any way that pleases you and plan to enjoy watching them for a few months. If they are almost mature, you might want to go for a more simple set up. When I want to encourage corys to spawn, I put them in a separate tank with just a half inch of sand or fine gravel at the bottom, perhaps a cave, and some kind of easily movable plants. The idea is that once they spawn, everything will be removed so that the fry can hatch in a clean bare bottom tank. Therefore, the more you put in, the more you will have to take out once the eggs appear.
I keep most of my tanks at around 76 degrees F., but it could be a little higher. Then when the time is right you can unplug the heater, give them a big water change and that is often all that is needed. In the morning, or after a day of so at around 72 degrees, once it starts warming up again they should spawn.
I would suggest that you concentrate on raising the spawning group well and condition them for a week or more on live blackworms, or frozen bloodworms, before you attempt to get them to spawn. If you are in a hurry and they spawn too young, you will have a small batch of fry taking up your tank, while if you are patient you will have a much larger one.