You will definitely need dedicated hosting for this, especially if you're planning on hosting the actual video files on your server.
Try not to get sued, too... Here...
IF YOU NEED PAYMENT/PAYPAL:
Go to your local gas station and get a "nFinanse" prepaid debit card. In order to link it to PayPal, you need to register it.. Which means you'll need a name, SSN and ID. You'll have to figure this part out, but if you're ballsy you could always search the http://ssdi.rootsweb.ancestry.com/cgi-bin/ssdi.cgi. Just put in 'Age of Death' and +/- a few years. Poof, a bazillion SSNs with names, addresses, etc. Once you register the card, you'll get routing/account numbers to verify a PayPal account (by bank account).
IF YOU NEED PHONE SERVICE/INTERNET:
Go to eBay and get some used Sprint phone. I always use the HTC Touch Pro for this because it's acceptable, I know it works and it acts as a 1.5Mbps router. Go to the gas station or Wal-Mart and get $60 of Boost credits ($50/mo for unlimited service [phone, web, messaging], $10 to activate a used phone). Call up Boost Mobile and have them activate the phone as whatever name you want. Roger Rabbit, Michael Jordan (mine is Stan Marsh), some reps will say they can't do it. Hang up and call back until you get one that will... Not to sound bad or anything, but if you get an Indian, don't waste your time (I've argued with these guys about activating an actual Boost phone, it's shitty outsourced CS and they're dicks.) You want a black guy, he DGAF.
If you're using it just for web, you can do prepaid instead of the $50/mo and unlimited web service will cost you $0.30/day. (Yep, unlimited, anonymous, 1.5mbps internet for $10/mo.)
If you use the HTC Touch Pro, just install the HTC wifi router and the phone will provide wifi for up to 4 devices. (Good for backup/rural internet anyways.)
IF YOU NEED HOSTING:
Go to kimsufi.ie, if you're American, you'll need to verify your ID/address by scanning & emailing a photocopy of a utility bill & DL.... Photoshop. Poof, quad-core (2.66GHz), 16GB DDR3, 2TB HDD, 100mb connection, 10TB bandwidth (extra BW is $2/TB) dedicated off-shore (France) server.
I was going to sell glass pipes online and this is what I did.

So I have an anonymous CC (that I can use at any ATM location) linked to an anonymous, verified PayPal paying for anonymous dedicated server which I can connect to through anonymous internet connection from anywhere there's Sprint CDMA (3G) coverage.