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The image you posted will look horrible when printed. The jagged lines will only get exaggerated. 300DPI is "photo like" quality and you would have to be within a foot to notice any of the small issues. So anywhere from 250 DPI to 300 DPI would work fine for you. The printing DPI is determined by the resolution of the file you want and the size in inches. So a 250 DPI 14X24 should be about 3500X6200 or for 300DPI, 4000X7000. Those are quite large pictures and if you can't find one that size just realize that you might see some artifacts when looking close.
I'm not saying this to add confusion or anxiety to what you print. In the end, as long as the picture is 1500+ pixels on both sides and no one is putting it in their face to look, it will look good and clear. Just stay away from brush stroke ones (unless they are a gigantic resolution) and anything with jaggedy edges.
The danbooru link would be good, except you might want to add a border, otherwise something will get cut off when printing, or the aspect ratio will be off and Dead Master will look three feet too tall.
This one would be good because even though it has brush strokes, they are small and not black on white, so they'll blend better when printing.
