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I am looking for a low resulution data set (grid) of the world that contains the elevation above or depth below sea level, respectively. For my purposes, it's enough if I can display the entire data set on a laptop screen. For example, with a 20 by 20 minute grid, that would be 1080x270 pixels. It could by slightly larger, though.

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You can use the ETOPO dataset by NOAA NCEI. It has a 1' resolution, which you can of course downsample according to your needs.

Several derived data sets are available as well.

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    In case someone is interested, I was able to downsample the data with grdsample ETOPO1_Bed_g_gmt4.grd -I0.30 -G0.30.grd to a 1200 pixel wide "image". – René Nyffenegger Apr 4 '17 at 6:19

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