I don't know about the expiry - that seems more like a programmatical function of your website.
Where I work, the software that clients most often request is
Red5. I don't know it, so I can't speak for it, but it seems to be what most people find appropriate.
One thing I'll say is, make very sure you know how much traffic you expect. How many visits, how many concurrently, how much bandwidth that translates to, and how much bandwidth you have available. I've lost count of how many times I've seen this bite customers in the behind.
One time, a internationally famous band (let's call them "the band") was launching a new album, and they had an interview on BBC radio one evening to promote it. They were also making the first track available for download. Their website was hosted with one of our clients, on a single Plesk server, behind a firewall that's good for 100mbit. The file was 7MB. As you can imagine, the moment they gave out the URL, the site disappeared from the internet.
Even if your traffic won't be too much for your available connection speed, it might still result in a huge bandwidth bill, so make sure you know what to expect.
You can always put your video on CDN so that it's served externally. Rackspace Cloud Files does this - streaming URLs with CDN support:
http://www.rackspace.com/blog/cloud-files-adds-cdn-video-streaming/
