I want a big hard drive contains all my stuff, which is about 2 terrabytes' worth, and another drive that is a mirror of it for safety. Then, I want each of my office PC, home PC, and laptop to each synchronize with a subset of the stuff on the big drive, and to each remain continually synchronized with their subset of the data on the big drive, over the internet. So for example, say I am writing a paper, and work on it in all three locations. There is only one copy of the paper on the big hard drive. There is always an exact copy of that paper on all three computers. If I change it from any computer, the new version is synchronized with the big computer, and the other two computers.
This is like having all your stuff in the cloud, constantly synchronized with all your computers, except using your own hard drive (plus a mirror backup of it) as the cloud, instead of buying space in the cloud, which is way, way, way too prohibitive for this much storage room.
Or, it's like having no hard drives in the computers, and just using a remote drive as their internal drive, except that would be too slow, so each computer's internal drive is an intermediate step for the data that lets that computer be fast.
For items like documents which you may actually be changing you could use livemesh which basically syncs between different machines. I use it between my work laptop/desktop and it works great. It does also sync things with MS servers. There are a few others which will do the same thing, thats just the one I happen to use.
For the larger items you would need to keep them in separate folders, and have it split into sections you wanted to sync with the particular machines. I would probably setup robocopy to run with the correct options for the copy / sync process to work as you needed.
I think this would provide most of what you are asking, but its a bit of a confusing request to try an think through.
You could set up the big machine with a mirror "raid 1". That means all data is always written to both HDs at the same time. You could then create short cuts to the shared big machine so that when you are working on any computer in the house you are always working over the network on the file that is stored on the raid. You will never have important info on your personal computer it will all always live on the big computer. The flaw to this is if you have a network issue while editing a word, excel or access file, you could risk corrupting the file.
Or you can get all crazy and and have multiple copies of important stuff on the raid and on you personal pc. This is helpfull because you have 3 copies. If the big computer gets hit by lightning or is stolen or something crazy you still have the file on your personal computer. You can manage the syncing and keep all files up to date and the same using Microsoft SyncToy. It is a free tool from MS for windows. It lets you sync folders manually or automaticlly any way you want.
My personal setup is an old p4 with a 2x 750gb in raid 1. I also have a 750gb in my regular computer. So all my important stuff like pics of the kid and videos, of wedding and stuff are saved on all 3 HDS. When I make a change I make it on my regular PC and then I maually launch SyncToy to make the 2 HDS on my P4 match my D: on my regualr PC.
I Suggest nightly incremental backups for the file server (over RAID1) since it'll provide you with a history of the files to prevent accidental deletion or saving work you really didn't want. Imagine deleting a file on accident, it gets synced to the server before you can stop it, and it is wiped out everywhere. The way my server is setup I have a copy of the file up to 1 month old and it uses very little extra space.
I use Live Mesh to sync important documents/photos between my various PCs and the cloud (Windows Live SkyDrive, 5 GB free). This occurs automatically, and needs no intervention on my part (does need an active Internet connection).
I use SyncToy to sync media files (music/movies) between PCs. This requires me to run the sync, though this can be automated.
Both tools are free, and are from Microsoft.
The drive mirroring you're referring to is RAID-1, where two hard disks are mirrored. This is a feature of your motherboard, and you enable it via BIOS.