If it will be in your basement I assume PC noise isn't an issue. In that case, the truth is just about any PC will do. I'm using a dual-core ATOM configuration as music server only and it does it's job with no problem. I've also seen single core ATOM netbooks work fine as music servers. So processor power isn't important - don't spend money on it.
However, since you don't seem to be looking for a "nearly free" alternative, I'd recommend the following:
Get at least 1GB of RAM (up it to 2 or 3 GB if you're planning on also using the PC to rip bit perfect copies with EAC or dbpoweramp). This will prevent memory from being an issue.
If you are going to access it remotely (remote desktop or web) I'd also forgo the video card - a modern motherboard will have all the functions you need "on board". You want the simplest PC that fits your needs - less complication, hardware, and processes will lead to cleaner output, and simplicity = fewer problems. Less heat = longer life for PC. So leave out any cards/hardware you don't really need.
I'd recommend a fairly modern (new or refurbished) PC, as your $500 will cover the cost no problem. With a new(ish) PC you can get better wifi/network features and performance, newer versions of the OS work better and are more secure, support exists, and you'll find it easier to work with whatever software or hardware you might want to in the future.
Update: I just looked on the Dell site, and they have multiple models -new - that would be good for you in the $350 $500 range. I also see that many come with Vista 64 - if you get Vista 64 you might as well get 4 GB RAM, as it can exploit it (Vista 32 can't fully exploit 4GB). Again, for music server purposes I'd go with the slower, cheaper processors.
