Home server does all of this and is £90 for the software.
It'll do block-level backups of all your PCs automatically and keep an almost infinite history, provide normal server style shares, web interface (including free domain name and SSL certificate) to all your files stored therein, remote-control any home PC that's on as well from anywhere, and file shares also have version copies meaning if you delete or change something in error, even a few weeks later, you can get back the correct version. And of course it'll do media streaming and all that kind of thing.
Backup uses de-duplication technology, so any block that's the same as on another computer takes up no space. They cite 10:1 compression typically with serveral computers connected.
No need for RAID - connect up more than one hard disk to your server and it will automatically replicate areas you define to be replicated. They if you run out of space, just plug another one in, that's it! If you wanted to take out an old one (to make room for a larger drive), just remove it from the pool, wait for the storage balancing to complete, and take it out again. All through a whizzy and very simple to use wizard type interface.
Also keeps track of hardware health of all connected machines, telling you if there's a problem.
You can also get add-ons for it - document archiving, numerous media thingies, off line backup etc etc.
If you or anyone else is seriously interested in WHS, it is available as either a pre-configured physical unit from HP or OEM software from ebuyer, who also have some proper HP server hardware very very cheap:
WHS:
http://www.microsoft.com/windows/products/winfamily/windowshomeserver/default.mspx
HP Server:
http://www.ebuyer.com/product/140153
Sounds a bit like a sales pitch - honestly, I have no commercial interest in it - just a keen user!
Here's the front page of mine, TalkTalk line permitting:
http://sittingbourneSPAMerver.com/