STEP 2 - OUTLINES
Click "Duplicate Layer" in the Layers box to create a copy of the "Background" layer and rename it to something like "Outlines".
Now apply the Ink Sketch effect to the layer. Set both Ink Outline and Coloring to "0". Your map should now look like this.
Now take the Magic Wand again, but set the Tolerance setting to something around "25". Click into an area that was water in the original map. If you get something like this
your outline has a leak somewhere.
A quick and dirty fix to this problem is using a Gaussian Blur. Set the Radius to "1". After the blur, try the Magic Wand again. Your outline now shouldn't have any leaks and your selection should look like this.
Another way would be to manually correct any leaks by using the Pencil tool.
Select the Magic Wand again, but now set the "Flood Mode" to Global. Click on any white area and hit Delete. This will remove all white regions and only leave the black outlines. Click the checkbox next to the "Background" layer in the Layers box and you should see something like this.
Finally, apply a Sharpen effect to your "Outlines" layer to pronounce the lines and remove some of the blurring. After that, you should have this:
The "Background" layer is no longer required. You can either delete it or simply hide it from showing (and keep it for comparison or future reference) by unchecking the checkbox next to it in the Layers box.
STEP 3 - LANDMASSES
Create a new layer and rename it to "Land" or something similar.
Now highlight the "Outlines" layer and use the Magic Wand to select any water areas. You may have to adjust the Tolerance setting until it works for you. Also, don't forget to select any lagoons and lakes, too. Then hit CTRL-I to invert that selection to get all landmasses. Your selection should look like this now.
Highlight the "Land" layer. Use the Colors box to select a fitting color (click the "More >>" button to get a detailed selection). I'm using #F4A460 for this tutorial. Now just hit Backspace to fill the selected area with your color. Use the "Move Layer" buttons in the Layers box to make sure your "Outlines" layer is the top most and you should now see something like this.
Go to the Colors box again, swap colors, and select a new primary color that goes well with your now-secondary color. For this tutorial, I'm using #00FF7F. Use the Magic Wand on "Global" mode to select all your landmasses on the "Land" layer. Now apply a Clouds render effect to your selection. Use the default settings and leave Blend Mode on "Normal". Repeat the Clouds render, but change the Blend Mode to "Multiply" for the second run. Your map should not look similar to this.
Next you need to apply some Noise to your landmasses. I'm using Intensity "33", Color Saturation "0", and Coverage "25". Following this, apply a Motion Blur with the default settings. And after that, use the Ink Sketch effect with Ink Outline "60" and Coloring "100". Your map now looks like this.