X-Plane is the best program I can think of off the top of my head to render/test aircraft, but:
Acquiring it legally costs money
There is a learning curve to using it. I haven't used in a while, and from what I remember it was fairly complex (it's been a few years since I used it).
As with the tank design, I think if we did a plane contest 1930s-1940s would be best. Having to design radar systems, electronics, supersonic aerodynamics, and all that would rapidly get too complex. Like the last contest, but worse.