Cigar Box Ukes are a fair place to start, because you learn the basics, including thinning a top, cutting the soundhole, making bracing, carving a neck, and perhaps most importantly, the geometry or math of the strings/nut/bridge. The only thing you don't have to do is bend the sides. Note that all of the uke kits provide already bent sides. That's right, this is just as good as a kit (perhaps I exaggerate, but bear with me...). Also, there's an historic place for the CBU, as there is a long record of broke-ass folks who wanted to have a guitar of some sort. Muddy Waters, BB King, and many more, have all constructed box guitars at one time or another. It's a time honored way to get started.
Here's a follow up for the OP, whatever box you start with, you should make sure it's about 2-3 inches deep (too deep and it doesn't fit under the arm comfortably and can lose volume, too shallow and it won't resonate and also lose volume), and for a concert sized uke it should be at least 9" long. Plan on removing the bottom and replacing it with quarter sawn spruce/red cedar and making that the soundboard.
