Jamieson, Fausset and Brown on Daniel 1:2

2. Shinar--the old name of Babylonia (Ge 11:2; 14:1; Is 11:11; Zec 5:11). Nebuchadnezzar took only "part of the vessels," as he did not intend wholly to overthrow the state, but to make it tributary, and to leave such vessels as were absolutely needed for the public worship of Jehovah. Subsequently all were taken away and were restored under Cyrus (Ezr 1:7).

his god--Bel. His temple, as was often the case among the heathen, was made "treasure house" of the king.