What's a great starter home stereo system?
Something high quality (with a subwoofer most likely) and reasonably priced. Not sure if 5.1 is needed. Probably just a 2.1 would be best. Any recommendations GDGT?
"High [audio?] quality" and "reasonably priced" are goals that are generally diametrically opposed to each other - particularly when it comes to stereo and home theater audio. With that in mind, you can maybe see why ajcohen's and frankspin's suggestions are sensible. Sometimes the correct answer is to not buy now, and save-up instead while looking for the lowest cost acceptable solution.
When you are just starting out, as your friend seems to be doing, it is easier to make a series of smaller purchases, and slowly grow your system until you reach a point where you are happy. By design, most HTIB solutions do not lend themselves to incremental upgrades - to upgrade any one piece requires replacing the whole thing. That should be reason #1 why you are not doing your friend a favor by going down that path. The other knock on HTIB, particularly on the very low end, is poor audio quality. The few positive reviews that I have seen are in the $400 and up range.
For an AVR brand that is bang-for-the-buck oriented, check out Denon. If she can afford a little more, try Onkyo. Alternately, headphones and something like astrogaming's mixamp pro (maybe paired with an HDMI switcher) can get her going while she saves for something better.
For speakers, she may want to try some of the suggestions of Steve Guttenberg (CNET) - news.cnet.com/audiophiliac/?tag=blgs.list
Of particular note are Steve's positive words for some of Monoprice's speakers and headphones.
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I don't know if you're going to be able to find a HTIB set up that supports airplay. They're meant to be simple solutions for people who don't want to invest the time and money into building their own AV set up. Your best bet would be to just buy a HTIB and stream the music via AppleTV which would output sound to the HTIB.
I'm making the above recommendation based of the fact there will be a laptop or desktop on to support streaming via AppleTV.
Pioneer has always made good stuff, and have been doing the Airplay since Apple announced it so they've got it down pat.
The great thing with this system for your friend is that they can start with only a 2.0 setup and then add speakers whenever they want. I did that for the last couple years and slowly upgraded my system, bit by bit.