You need a PSU, that is what will distribute power to the various parts of the PC. A UPS is optional although in areas like where I live where the power grid is unstable, a UPS can go a long way to keeping incoming voltage fluctuations in check. A UPS will not negate the need for a PSU.
While on the subject of PSU's, think of the PSU as the heart of your computer, everything depends upon it, it is not a component to cut corners on. A quality PSU will go a long way to keeping your PC functioning happily