I may also want to be able to use something like Air Video Server to allow said son to watch streamed movies on his iPad, but that's not a must have.
Once you (or he) starts using it, I suspect you'll find it an indispensable app--being able to access every file stored in the house, then initiate a seamless live conversion so it can be streamed to the iPad--and then optionally AirPlay'd to an aTV2--is something I got spoiled by very quickly. If you have Airport Expresses in some secondary rooms (bedroom or kitchen for instance) where you also have a TV or display, you may prefer an aTV2 there simply as an AirPlay destination for both audio and video instead of just audio.
Which Mac mini should I look at? Is an older generation okay (there are mini display port + audio to HDMI adapters for sound)? If I need to look at the current generation, would I be fine with the basic model (integrated graphics) and extra memory?
You didn't mention what you'd be hooking your mini up to, as in which HDTV, whether you'll go through an AVR, etc, but now that I own a mini w/ HDMI, I wouldn't consider one that did not have HDMI built-in, it's been a blessing in terms of home theater and great not having to mess with special adaptors. With my 2011 mini the HD 709-A profile over HDMI is very nice. Of all your requested tasks, the two most challenging are the 1) 1080p bluray rip playback with XBMC/Plex and 2) Hulu desktop, the quick answer is anything back to 2.53 2009 would probably serve you impeccably well, but I would only do a 2010 or 2011 and unless you happen upon a great deal for a 2010 go with the 2011.
Why? My opinion has remained essentially unchanged since the 2011 minis were released 6 months ago: unless you need an optical drive built-in, why even consider buying an older generation model when used prices are still so relatively high for them compared to buying the 2011 model new, let alone buying the 2011 model as a $519 refurb or <$500 warehouse deal from Amazon?
My one concern for you, as a fellow owner of the base model 2011 upgraded to 8GB RAM inexpensively like oceanjumper, is whether its stock 5400rpm drive will be up to all the multi-tasking you plan for it? So factor your time and skill and willingness to do upgrades yourself vs. purchasing a more expensive model upfront that likely won't need an upgrade when you try to calculate the total cost of the models you're considering. In my case, I already had an Intel SSD, a 500GB Scorpio Black and a 500GB Seagate Momentus XT on hand, any two of which I was willing to install in the mini myself once I got it for our living room. You may not want to take that risk, and with hard drive prices still at a premium, it may make more sense and be a better value for you long term to buy a model with the two 500GB 7200rpm drives already inside.
I have owned plenty of C2D Macs and the entry level i5 mini was a significant, undeniable step up computationally. You didn't mention what else you have in the house, so for instance, another reason why you may want to step up to a better, more expensive 2011 model is if you plan to use it for all your transcoding. Do you have something else that you'll run Handbrake on? With even the base 2011 model, it's also nice knowing that under the hood you have the horsepower to play back the toughest blu-ray rip just with the CPU, i.e. with no acceleration or graphics assist needed.