What type/size server would I need to handle the traffic from a viral video?

Hello, I have a video that is going viral, and may go viral in a big way. It will probably end up on the news, and possibly large news outlets. At the end of the video people are directed to my website, which is currently on a shared hosting plan through godaddy.

As it is right now, if a large amount of people try to access the site at one time, it will probably crash the site.

I'm trying to figure out what size server I will need to handle many connections at one time, which I think is referred to as "concurrent connections".

The website has videos on it, but they are embedded videos from youtube, so if people watch the videos on the site, it should not pull extra resources or bandwidth from the site. There is nothing on the site that will pull additional bandwidth other than regular viewing of pages.

Can anyone tell me what is the cheapest option of a type of server that would be capable of handling many visitors to the site at one time? I'm looking at Virtual Servers and Dedicated Servers, but dedicated are quite expensive, and according to Godaddy, you have to hire someone who charges a fortune to even put your site on something like that.

Can anybody point me in the right direction? I need to be dealing with this as fast as possible, but I don't know exactly how to do it.

Thanks,