All projections cause distortion. In my opinion, equirectangular is the most straightforward to make, especially for a beginner, and it can easily be converted to other projections by a free software program.
NASA GISS: G.Projector — Global Map Projector
With this, you don't have to estimate the enlargements at the poles or the distortion of the continents. It will convert a map that is in a 2:1 ratio to many well known projections.
Now, how technical do we want to get? If we just want to show the continents and the relative distances between them, you don't have to do much else. Just be aware, as I said earlier, that the areas at the poles will not be 100% accurate. That's not too bad if you don't have much in those areas.
If you want to be totally accurate, there are ways to correct those polar regions. I use Photoshop. I'm not sure if Gimp has the same function, but here's what you do.
1) Take your equirectangular map and use Photoshop's polar coordinates filter to make your rectangular map into circular ones with the poles at the center, just as you see above.
2) Use whatever tools you're comfortable with to blend textures, move lines, and adjust things at the poles so that they don't have that pinched centerpoint.
3) Now run the filter again, but in reverse, from polar back to equirectangular.
4) Your new equirectangular map now shows the areas at the poles properly stretched so that when you apply the map as a texture onto a sphere in a 3D program, everything will look correct. The continents will narrow as they get closer to the poles, but at least things won't converge in a point.