DFT calculation on Sn and/or SnOx

Dear MaterialScience friends,

I’m asked to perform a DFT study on Sn and SnOx surfaces.
Since this is a complete new field to me, I’m looking for experts to share experiences.

I will start working on beta-Sn, also called white tin or metallic tin.
The first thing, I like to explore, is the DFT optimised lattice constants a and c.
In the past, I did a Birch-Murnagan fit on fcc metals, that boiled down to a two-dimensional fit of Energy as function of cell volume. The latter could be substituted by lattice parameter^3.
Now I need to do this in three dimensions. How is this generally done?

Secondly, beta-Sn appears to be paramagnetic. Shall I do above optimisation both spin-polarised and spin-unpolarised and compare the results?