Yes, you are spot on.
The net ionic equation for this redox reaction looks like this
The more reactive zinc will remove the lead (II) ions from solution.
Notice that the oxidation state of zinc goes from zero on the reactants' side, to +2 on the products' side, which means that zinc is being oxidized.
The oxidation half-reaction, which takes place at the anode, will look like this
On the other hand, lead's oxidation state goes from +2 on the reactants' side, to zero on the products' side, which means that it is being reduced.
The reduction half-reaction, which takes place at the cathode, will be
The cell potential will be