So yesterday morning I stumbled across tinkercad.com, a simplified 3-D modeling tool that is completely browser-based. I signed up for a free account, did a few tutorials, and within less than two hours had made a 1/3000 scale spaceship.
Admittedly, it's not super-detailed, but I achieved the basic shape I was looking for. And the simple lines compare fairly well to the earliest Star Fleet Battles figures, which was what I had in mind as I did this.
With a couple clicks I could export my work as a .STL file. The next obvious step was to go over the shapeways.com to see how easy it would be to get a plastic version printed up. It only took a few minutes to make an account and upload the files.
The based version would cost nearly twice the unbased one. So this is why most Shapeways Marketplace stores sell spaceships unbased (that and a lot of people are fussy about the bases they use). Admittedly, I could bring the price down with further tinkering. My base is 5mm thick, which is way more plastic than is needed. The peg could probably be slimmed down as well.
If I could do this with a couple of hours, no prior 3-D modeling experience, and no real talent for visual arts, then there must be a ton of people out there who could do more impressive work with this tinkercad tool.