I confirm that GEBCO data base is the mostly used source of data for your purpose. I use it for oceanography in the open ocean and I am quite pleased with this product. Note that the French Navy (the so-called SHOM) has its own data base, but it is not so easy to get the data.
SRTM is another option (Shuttle Radar Topography Mission). The bathymetry is a composite of Smith and Sandwell 1 minute grid, multi beam and coastal relief models.