Rowly, I would not recommend using a cardboard box. Believe or not, they will eat right through it once they are a few weeks old. I use a simple plywood pen 3' high and about 60 sq ft. As for the 4 week transition, why don't you make a simple chicken wire enclosure. I use 3' chicken wire loosely fastened to T posts which are just set about 9" into the ground. Easy to put up and take down and it beats rowing to the island every day. I would recommend that you get a copy of Storey's Guide to Raising Poultry, good info and reference book.
As to incubating eggs, now you are in a whole order of magnitude higher level of complication. When you have a random group of ducks, it is almost impossible to coordinate hatching times neatly. This means that you will have eggs of various ages in the incubator at any given time. The best type of incubator to use is a circulating air type with an automatic turner. You really don't want to get involved in having to turn eggs every day. Now the complicator, eggs must not be turned during the last 3 days and they require a higher level of humidity. That means a second incubator! I use Hova-Bators, simple, and dependable and cost about $140 US. There are usually some available on Ebay. A web site that will give you more data on incubators is mcmurrayhatchery.com. Unfortunately, everything in life tends to get more complicated as you delve into it:)
Have fun!
Jim
