Contrary to what you might think, we are actually going to use http instead of UDP. You can either use plain HTTP or Dynamic Adaptive Streaming over HTTP (DASH).In this way, different versions of the videos (bit rate) can be distributed as per bandwith.A manifest file is provided for these video versions for the client to pick on.
Assuming you don't have a huge load of lawyers, so not much hould lead to you. If registration and/or payment is to be done, then you won't trust any one with your money so a server for this will be managed by you.
I suggest pay for cloud space, this is where your videos will be initially uploaded, formatted into multiple versions of both audio and video at multiple bit rates, and finally uploaded to your different CDNs(third party).
To reduce the load on a single server and many other factors, i suggest you employ third party Content Distribution Network (CDN)/s like Limelight, akamai and Level-3. These server clustersif brought near tier-1 and/or Access ISP provide for high-speed streaming of videos.
But you could save yourself the trouble and set up a P2P video on demand network like PPTV, PPs, et-la.