Physical state of hydronium
This is a bit touchy.  The problem is that a bare proton, $\ce{H^+}$, won't exist in water.  It attracts electrons too strongly.  Once this was recognized, chemists started to write the bare proton as being bound to a water molecule, thus $\ce{H3O^+}$.  However, studies also showed that water molecules are typically linked together in clusters containing a fair number of water molecules held together by hydrogen bonds (Google for this if you are not familiar with it).

Thus today's version really is $\ce{H+_aq}$ but that looks awful, so it is as you note $\ce{H3O+_aq}$ is more often used.

The important point is that how you write it isn't really important.  It is the realization that the bare proton attaches itself to any nearby source of electrons.

How you should handle your homework depends on what your teacher does in class.  I'd follow that example.