I would suggest you find out what delivery format youtube expects. is it a flash based? something else? Then go and find a live encoder that will take your video signal and process it into that perticular flavor. there are many companies that make hardware to do this, but you'll want to make sure that it can do the specfic format your host wants.
It looks like it depends on what platform your going to run it on windows or Mac? but i did a quick look at adobes website, it looks like there are a varity of capture cards that are compatible but my guess would be to get one of BlackMagic's Decklinks. That would give you a plethora of input choices.
Now that would only give you one source going from the camera directly into the Decklink, if you wanted multiple sources, like multiple cameras you are going to need a video switcher, or something to act in a similar fashion. are you planing on more then one source?
depending on your price range you may look and see if Roland has anything, you may also look at Blackmagics new switcher line up the ATEM Television Studio might be something that would for for you as well.
If you have a bigger budget i would look at getting a Tricaster instead. it is a all in one switcher CG tape playback and streaming unit. for me this is the best bang for the buck for small productions