I've never built a server on that scale, but most distros will run the apache web server out of the box, so getting ~4Tb's worth of files online isn't much harder than getting them all in one directory structure.
For a that size, I'd have one partition for all of the files [EDIT: given the previous post, check that the distro will support this first. I think most newer kernels will, but it may depend on the filesystem.], and mount it as something like /usr/share/httpdocs, and point your documentroot in httpd.conf to that address. If you're going to be saving files to the web-partition a lot, then use a journeling filesystem (I suggest reiserfs), otherwise don't (use ext2) as you'll use the disk space more efficiently.
If you want to stream over protocols other than HTTP, then Apache won't help you; you'll need to look at a more appropriate server (try searching www.freshmeat.net
You might also want to consider using software RAID; distros like SuSE will set that up out of the box (in an advanced install), and you can gain speed and/or reliability savings by trading off disk space. RAID (or LVM) will also let you combine multiple partitions into one big one. Hardware RAID is an option, but check the distro's HCL (hardware compatibility list) to make sure that it will actually work (I say that from experience!).
Hardware: Get a box with one processor, and don't go for the fastest you can find. The disk or network speed will probably be the limiting factor. 64-bits won't help you here (unless you want to move the entire 4Tb of data into one tmpfs (in-memory) partition, in which case if you want more than 4Tb of RAM, so you'll get a speed benefit from the increased native address space).