Although not listed exclusively, I'd imagine a video game falls under the general umbrella of an audio/visual work. You can see there that the fee would be $45 along with the completed forms and a copy of the game. This is the one I used to get my movie copyrighted.
http://www.copyright.gov/register/performing.htmlAnd here's the full list of forms incase you want to see them.
http://www.copyright.gov/forms/As for your company, this place looks kinda promising. Although I wouldn't worry about going through the hassle unless your company starts earning money and you have to deal with taxes. Currently my movie "company" isn't official, cuz its not made any money.
http://www.legalzoom.com/legalzip/business...0220407&sRefer=