I'm not sure where you're seeing the $519 refurbished + full warranty deal, though. Through Apple? If so, they're out for now...
yes, via the Apple store website, grubavs has kindly posted the direct link, the way Apple refurbs work is if it is in stock, it's displayed, out of stock, it won't even be listed. If it isn't listed when you try, try back in a few hours and it just might be there.
I don't have the mini in my possession, but I found a refurb with the specs I posted for sale for $250 which seemed like a pretty good deal...I hear what you're saying, though, and it sounds reasonable to spend an extra $200 or so for something much better.
You can get a better Mac for that same $250: I picked up a 2.0 C2D Macbook in perfect shape 4-5 months ago for my parents for less than $250. Every one has to make their own decision whether it's better for them to spend ~$250 or $450+ and I don't think there's one clear answer, it's going to depend on a lot of different factors and that's why we like discussing these things, to help make choices. (In your case, a $250 or so used Mac as an iTunes server allows you to pick up an Apple TV ($85) or two and/or an Airport Express ($69) and come in very close to what you would have paid for that newer Mac by itself...not a bad tradeoff for some.)
In your case the first performance hurdle you have to clear in your mind is why just limit yourself to audio streaming--why aren't you thinking about whole house streaming and playback of audio and
I realized I didn't answer your question about the minimum requirements for your needs, so if you're really looking to save money, to spend the least amount possible on a quiet, low profile Mac to host your iTunes library and serve it up to other devices, I'll be a little more specific...I'd start your used search with the 2009 Minis, I believe they were the first Minis to get n wireless and I think they have some good life left in them. But something else, somewhat outside the box to consider, a Macbook circa 2007 would function as your networked media server as least as well, if not better, than the 2009 Minis--and they're much better than the core duo Minis--and used prices have really fallen on older plastic MacBooks. First, it's a laptop, so you can take it with you, if you don't also have a laptop or iPad, all I'll say is mobility is nice. Like the 2009 Mini, those old MacBooks are also C2D and n wireless, but unlike on the Mini it is extremely easy
to upgrade both hard drives and RAM in a plastic Macbook--pop the battery, remove 3 screws, both the RAM and drive pull right out. After initial setup they run with the lid closed just fine, and a 2007 Macbook can run Lion, if that matters. You can also replace the crappy optical drive in those MacBooks with a second hard drive using a very inexpensive tray adapter, which means you could keep a copy of your large iTunes library right there (in the Macbook) and wouldn't need an external. That maintains a slim form factor and saves some money if you don't already have an external enclosure.
Since your priority seems audio streaming, I can't stress enough how valuable it is having multiple copies of your iTunes library.
I see relatively inexpensive MacBooks used on Craigslist and eBay all the time, I almost never see inexpensive Mac minis, so perhaps give it some thought--an old cheap Macbook could be your inexpensive whole house iTunes media server at home, that you could also pack up and take with you on the road
should the spirit move you. If you go the Macbook route, here's exactly what I've done to my old warhorse of a 2007 Santa Rosa Macbook:
1. Make sure it has at least 4GB RAM (mine has 6GB but then I often asked it to play HD video while multitasking)
2. Boot it off of a small, affordable SSD (I've had both an 80GB Intel 320 Series and a 128 Crucial M4 in there)
3. Replace the optical drive with a large 2.5" drive partitioned in two, one a clone of your SSD boot drive, the other your entire iTunes library, that way you have some redundancy if your boot drive fails (I have a 750GB Seagate Momentus XT in there at the moment, with a clone of my lossless iTunes library (640ish GBs) plus a bootable clone of the SSD.)
This strategy isn't for everyone, but I already had the Macbook, I already had plenty of drives and SSDs to repurpose, and it was my main HTPC in the living room for a few years until I really started to get into blu-ray. (I don't sell my Macs, and usually hold on to them for a long time or pass them on to family.) Anyway, that old Santa Rosa Macbook got new life with an SSD, and souped up the way it is functions essentially as a backup and drop-in replacement for the 2011 Mini in my living room, which can also go on the road with me when traveling, visiting relatives, etc.
Once people realize which older machines can't be upgraded to Mountain Lion, prices will fall even further.