I'm looking to building a home server, but not really sure where to start. Here is what I would like to do:

- Store my data
- Stream media to my home network, or from someone else's.
- Remotely access and manage

However, on initial research, there seems to be many options and technologies out there: Windows Home Server, all the different Linux distributions, FreeNAS, Amahi, XBMC, OpenELEC, Greyhole, ZFS, RAID, Samba, etc... It's a bit overwhelming.

Any one ever work on a project like this before and have any advice?

I'm not really concerned about silence or hardware at the moment, as I am just repurposing an old computer. The only thing I'm actually buy are new 3TB harddrives.

Unless you are already knowledgeable in Linux (or want to invest a fair amount of time and become knowledgeable), probably Windows Home Server is a good solution.

I would have also said Win Home Server until a few weeks ago. You have mentioned quite a few options and I agree with m0002a that if you aren’t ready to spend a decent amount of time learning the ways of Linux servers, then Windows is a better option.
I had a server based on WHS v1 since fall 2010 that went flawlessly, no hardware fault and no major software problem, nothing that didn’t vanish after a RDP-commanded restart. The only problem of WHS v1 (and maybe v2?) is how it manages faults. My WHS installation simply didn’t boot one day; I suspected the OS drive, but that turned out OK, so in the end I had to reinstall the OS. It was impossible to recover the data from the 2 data drives because WHS organizes bits in a “virtual” way, aka the OS drive has a map of where files are – when attempting to recover the files from the data drives you’ll find all files in the root without any folders, just a huge bulk of files with no organization whatsoever. Being paranoid I had an external HDD of identical size as the two data disks that mirrored the data on the server, so I could restore everything properly.
Now I simply use XP on the server, an old copy that made way for 7 on my gaming rig. I also use an old PC, it doesn’t have motherboard RAID, and so I use a free piece of software called Syncron to sync my 2 data HDDs once a day (can be made to sync as often as you want, even right away). I have password-shared one of the data drives on the network. There is no disadvantage that I can see to using a regular OS on a home server; you can install regular AV/AS, mirror files on many disks, use cloud-storage clients, share printer and serve any file – most of these tasks are more difficult to configure on a home server.
So bottom line is that I highly recommend a regular OS coupled with programs like Syncron to enhance the functionality.

P.S. First post on SPCR, long time lurker on the forums and the site

Unless you are already knowledgable with Windows servers, probably Linux is a good solution.

Seriously, if you don't want to learn how to configure and run servers, avoid generic Linux distributions.
What you want in that case is a turnkey thing, like Amahi or FreeNAS (there are others). I've never used a turnkey thing because it's no big deal for me for configure and run a little server. So I can't recommend one specifically.
All the other names you mentionned besides Amahi, FreeNAS and WHS are either for HTPCs or too technical for you to bother with unless you really want to.
And unless you really want to get technical, I specifically recommend avoiding RAID and ZFS. Backups are paramount.

If you want to use free software and are lost, perhaps you should go to a meeting of free software fans close to your place or simply get in touch with the group running such meetings over the Internet. Some of these groups are friendly to newcomers and would help you. And it's sometimes easier if you can meet physically.

That said, it's really not that hard to set up a home server, whatever you choose to go with.