What is the difference between DFT and spin polarized DFT? Will it matter which one I use if I am only after the band structure and not the magnetic properties?
One of the differences of DFT and spin-polarized (SP)-DFT lies in the exchange-correlation functional which is spin-density dependent in the SP-DFT.
If the considered materials are not magnetic, both kinds of calculations in the end will be the same because the spin-density "dependent" exchange functional will converge to the spin-density "independent" exchange functional during the minimization process.
However, if the material is indeed magnetic, then whether you are after the magnetic properties or not, it's necessary to use SP-DFT because the spin-up's band structure of the spin-up may be different from the spin-down's one. The worst scenario is that when you have half-metals in which the spin-up electronic structure has the transport property opposite to the spin-down one (conductor vs insulator).
So first you need to know what materials you want to calculate and later decide which kind of DFT you want to use. If you don't know anything about your materials, it's quite safe most of the time to start with the SP-DFT. And after looking at the results of both spins, you can decide whether you should continue using SP-DFT or just the "regular" DFT.