This is pretty straight forward. The traditional map is very good for longitude and latitude. It's pretty lousy for the shapes and sizes of the continents cause everything close to the poles is expanded.
A more accurate map has to look like a carved up sphere on a flat sheet of paper.
This one claims to be the most accurate: http://imgur.com/gallery/O6lCFWC
Here's another nice accurate one but, I think, harder on the eyes.
Any 2D map that bulges in the middle is significantly improved over the traditional flat map.
and I like this method as a clever heart shape, which more accurately shows the countries in real size.
and the Peters projection is sometimes used but I don't like it because it doesn't accurately show the shapes of the nations near the poles. It flattens them when it should squash them so in some ways it's even less accurate. link here
I think the most accurate are easily the first two, or just use a globe and a 2D map, knowing it's inaccurate. All this is easily available with a quick google search "best 2D world map".