What I like about the NAS is that they are designed to run 24/7 without the headaches that keeping a Windows PC does.
I'm sure that using a NAS was an interesting project, but isn't the key difference between using a Windows PC and a typical NAS that the latter runs Linux. And there are much cheaper ways of running a small Linux computer than repurposing a NAS, most obviously using a Raspberry Pi (as mentioned upthread) in some shape or form, or some similar single board computer.
An RPI can indeed be cheaper. However, depending on the RPI's configuration (power source, case, memory, fan?, etc.) and how OP plans to use the website, resources allocated, maintenance, security, etc. things can add up quickly.
A Synology DS223 diskless + two 500GB HDDs are approx. $350 and it can be setup using the company's SHR, which automatically mirrors the content of one disk into the other, thus providing a fail-safe solution in case of disk failure.
Anyway, I just mentioned that as an option to OP, since I don['t know what kind of reliability he wants and his budget.