Which of the following structures is the most preferred and hence of lowest energy for $\mathrm{SO}_3$ ?

Formal charges help in the selection of the lowest energy structure from a number of possible Lewis structures for a given species. Generally the lowest energy structure is the one with the smallest formal charges on the atoms. Formal charge on an atom : $=$ total no. of valence electrons-non-bonding electrons $-\frac{1}{2} \times$ bonding electrons. For Lewis structure of $\mathrm{SO}_3$
Formal charge on $\mathrm{S}$ atom $=6-0-\frac{1}{2} \times 12=0$ Formal charge on three $\mathrm{O}$ atoms $$ =6-4-\frac{1}{2} \times 4=0 $$