Apache is a HTTP server. It means it's for websites, not file streaming. It just won't work.
The easiest solution for your problem is probably Dropbox. Just create an account and send your friend a referrer link, after he registers using that link you'll both get 500 MB extra space (that's 2,5 GB for free). Then you both install the Dropbox app. One of you creates a folder and shares it using Dropbox's sharing option. Any time one of you drops a file into the shared folder, it will be synced to second one's computer.
There are many other solutions like that, for example SkyDrive or Box.com, although Dropbox is my preferred one.
This approach has one drawback: all files will be synced between your computers, it means those will take up hard disk space on both computers. But storage space is cheap nowadays and there's a number of advantages: both of you have instant file access with zero waiting time (which just can't be achieved with file streaming over the net), not to mention that you don't have to set up a separate machine and don't have to spend a penny on entire thing.
By the way, setting up an always-on server on a retired PC is never a good idea. Standard PC PSUs aren't designed for constant usage and will die very quickly. You also need some space for a PC that will always generate some irritating noise, gather dust (which kills fans) and consume electricity.