As for the band saw, this is a tough question. Also if you start out using the saw there will be little likelihood that you'll learn to do these things without it. If you do learn to really cut glass first you probably won't use the saw much. After about 25 years doing glass we brought in a demo model saw about three or four years ago. It pretty much sits unused.
Some shapes are just unstable and are future broken pieces waiting to happen.
I recommend that you invest in a regular water fed glass grinder and save on the saw. The instructions say to use a wire along the edges and in the corner to prop the glass so there is no over lapping. The inside looks fine. No, you do not want the corners to overlap. If they did the box would be weakened.