If you like the idea of the convenience of streaming music, I'd say it's worth looking into for your music needs, but there won't be a streaming solution that rivals the video and audio experience of Blu-ray for quite some time (due to the vast amounts of data involved with Blu-rays). And since ripping Blu-rays locally and streaming them is also illegal (and not a particularly simple solution as yet), this is also something I wouldn't really recommend going down at this stage. So it's fairly safe to say that, for the moment, your ideal home cinema will need AV amp + 5.1 speakers + Blu-ray player.
Back to the music side - lossless downloads are also still thin on the ground - there are a few sites doing them, but it certainly isn't mainstream. There are rumours that the Apple store will soon incorporate lossless or even hi-def downloads, but I don't think there's anything concrete around this as yet (feel free to correct me anyone that knows different!). There are services like Spotify and of course Apple's iTunes Store though that offer compressed music, but still of a reasonable quality, though not CD quality.
Having said that, there's certainly good reason to put in a music streaming solution, since it's now very easy to rip CDs and then use one of the various music streaming solutions to easily have access to your entire music collection at the touch of a button. Ripping CDs is still technically illegal in the UK, but the music industry as a whole have now stated they won't be looking to prosecute anyone who does this (unlike ripping DVDs or Blu-rays) so that's pretty much a statement that it's legal in all but name.
You've mentioned Apple which do a number of options for streaming - with your budget you could easily look at the Sonos system though which makes it easier to store music on a NAS (Network Attached Storage) and access it without having to have a PC or Mac switched on. If you really like Apple, their Airport Express or Apple TV2 systems allow you to stream your iTunes collection and control everything with an app on the iPhone or iPod Touch, but this does require your iTunes is running which means having a PC or Mac switched on. Alternatively, you can try and track down an older Apple TV system which has a built in 160 GB hard disk, meaning you can at least stream your music without iTunes running. You'd be advised to check out the current issue of What Hi-Fi which has a big article on streaming music and covers these solutions in more detail.
Finally, on what kit you want, if music is your main preference, you'll want to have a stereo amp in there somewhere. You could invest all your money on just a stereo system and then just plug your Blu-ray player into this for movies. This means you can spend a significant amount on this stereo system to get the best possible music playback, whilst still having a decent movie experience. However, if movie performance is not far behind music performance in your priorities and you want 5.1, you could either have a completely separate system i.e. 5.1 speakers plugged into AV amp and separate stereo speakers plugged into stereo amp, or you could look to get an AV amp with front pre-out sockets (most middle to high range AV amps come with these). This allows you to connect the front speakers to a stereo amp and have your streaming solution hooked into this, meaning your music system is isolated from your home cinema and ensuring you get the best sound you can from this. For movies, you connect the front pre-out sockets on the AV amp to your stereo amp (either via dedicated sockets for this task or via another free input on the stereo amp) and then connect the centre, rear and sub speakers to the AV amp along with the Blu-ray. This has the benefit that you can utilise the same front speakers as you use for the music system as you do for movies, saving some money and space on extra speakers.
So a lot of options to think about! Feel free to come back with any questions / clarifications on what I've said!