Should the primary winding of a transformer have more or less resistance to increase efficiency?
I think you are on the wrong track with this question. The primary winding should have ideally zero resistance but it needs an impedance to prevent it shorting out the AC power applied. So, it has inductance and, for a typical power transformer that might be in the realm of 10 henries for 50/60 Hz applications.

The transformer equivalent circuit is shown below: -



With the secondary unloaded (not connected to a load) the primary impedance is due to \$X_M\$. Core losses and other resistive losses are shown as resistors. Leakage inductances are shown as \$X_P\$ and \$X_S\$.