If you just wanted a Mini to run 24/7 as an iTunes home sharing media server, and had something else to do the more labor intensive transcoding and conversions, then yes, even a PPC Mini would probably suffice if you will only be serving one file at a time to one device and both were wired--you can run a version of iTunes on 10.5.8 which supports home sharing, I do on a G5 PowerMac, and home sharing is what you'd need for an Apple TV.
I think the most pressing issue is to decide for yourself the value and risk of spending x amount of money for older hardware (and the old software it'll run) at this point. If someone were giving you an old mini, then certainly there's no risk in testing it, but things go wrong with older hardware and ideally you'd want to set something up once and then forget about it. So, it's a risk-reward thing, your best best would probably be to get the best used or refurb Intel Mini you can afford, I'd go with the newer aluminum styling, it'll have gigabit, run cooler, have faster wireless, be more efficient, and it's easier to upgrade the hard drive and RAM, etc...whatever you get I'd recommend you wire up both your Mini and your aTV and not rely on wireless. And, if you got a relatively recent Mini at a good price you could always repurpose it later if your needs change and you decide to embrace a more full-blown HTPC approach.
For any real help you'll have to define those "good prices" and "good deals" on specific models a little better. That's not enough to go on in the abstract. Also, you haven't mentioned where your media will reside, i.e. where it will be stored, do you already have enclosures, drives, etc. because that might influence which Mini might be best for you. But in theory, I do agree with your thinking here--I've always thought a Mini would make a great whole house iTunes media server for someone eager to play by Apple's rules. When you leave iTunes open on a wired Mac running 24/7, and you have a bunch of other Macs and iOS devices in the house, everything is much more smooth.