If you want to get in-depth information from XPS you should consider doing angle-resolved measurements (ARXPS), provided your sample is flat, smooth and large.
Assuming a standard lab-based XPS setup, the Zn2p peak will be most surface sensitive and the Zn3d peak will be the most bulk sensitive. The inelastic mean free path (IMFP) of the Zn2p peak will be around 7 Angstrom and the IMFP of the Zn3d peak will be around 20 Angstrom (assuming Mg-excitation and using the predictive formula by Tanuma, Powell and Penn for elemental Zn).
You can estimate the IMFP by simply looking at the universal curve (https://en.wikipedia.org/wiki/Inelastic_mean_free_path) or using the "NIST electron inelastic-mean-free-path database" (https://www.nist.gov/srd/nist-standard-reference-database-71).
PS: It's not the penetration depth of your photons that determines the depth resolution (this is usually in the order of µm), it's the escape depth of your photoelectrons.
Zn 2p has a binding energy of 1020 and 1040 eV. With Mg excitation (1250 eV) this gives kinetic energies of the electrons of 230 and 210 eV, whereas Zn 3d has 10 eV binding energy and 1240 eV kinetic energy. Except for very low kinetic energies, the escape depth of electrons increases with kinetic energy, as shown by the universal curve from Shirley or the more detailed ones from Tanuma et al.