You are right that alot of HTIB's sold these days are complete crap. To avoid getting a piece of crap you should avoid no name brands and stick to the big ones. (Sony, Pioneer, Samsung etc.)
You will not need a computer period as long as you have the reciever and cd/dvd player (I assume they will be using CD's to play their music?) Nothing to worry about right now because most HTIB's come with everything you need, including a cd/dvd player unit.
One thing to look for in quality speakers is that they are 2 way, meaning that there will be a tweeter and a midrange/woofer built into the tower of the speaker so that you can have clear crisp highs and lower range sound as well.
Some cheaper ones sacrifice a tweeter which still may offer OK sound but may not offer crisper highs.
To answer your question about the music playing you can choose modes on the receiver to different styles. For example, our Pioneer HTIB came with a neat reciever so it has options for music, games, movies, etc. and you just set the option and it will take care of it. Whether the music plays as 2.1 or utilizes rear speakers as well it will not matter because in a good system the 2 front speakers and sub will be more than enough for listening to music.
So basically look look for a system that includes a CD/DVD player so that your parents can play all of their music CD's without the need for a computer. IMO it makes sense to go for the HTIB because you get everything that you need with it (some do not come with all the hookup wires though). I don't know how your parents store their music, whether it be on CD's or some other way but it may be good for you to know that quality receivers will have many A/V inputs so that you can connect MP3 players, Ipods, Cd players, basically any external device to your liking. Also some of the newer systems come with USB ports on the front so you can play music off of a memory stick.
To sum it up look for a name brand product with high continuous wattage and 2 way speakers with lots of different types of inputs.
EDIT: The Onkyo system looks excellent, Onkyo is well known for their high quality HTIB's although it does not look like it includes a CD or DVD player (am I wrong?) Either way I'm sure it would be easy enough to get one and add it to the setup.
