The reason I find it easier to start with the sphere is because every projection will distort the actual shapes in question. If you look at an equirectangular projection of the Earth, you see Antarctica stretched out across the entire bottom part of the world. If you look at a polar project, though, you see its actual shape:
Now, knowing Antarctica's shape, how difficult would it be to draw it down there at the bottom of the equirectangular map? Pretty darn hard, in my opinion. You can mitigate the problem by using a different projection, but ultimately you're going to wind up having to make some kind of compromise of some shape or distance.
Now, 3d software isn't necessarily out of reach, even if you have no budget, though you'll be trading money for time spent learning. Blender 3d is free, open source software that has tools to directly paint on a mesh and unwrap to a texture. Here's an overview of the feature:
https://wiki.blender.org/index.php/D...tures/Painting
You won't get a detailed map that way, but you will at least be able to do your layout so that you can reproject and then work on a flat image.