This is not a good idea unless you really know what you're doing. High capacity batteries and high power circuits are pretty dangerous and there's a surprising amount of complexity to build a reliable UPS. You'd probably have better luck modding an existing UPS (say from a flea market) to use a bigger battery if you are really desperate to save every dollar.
Plus making it yourself you probably won't save any money unless you already have all of the tools required, which is pretty extensive if you wanna do things right/safely.