Regarding IP issues to consider:
Copyright:
Don't dismiss the thought of using copyright to help protect the website. While Artchain is quite correct that copyright won't protect ideas, it does protect how those ideas are expressed--the actual words you write, artwork you may use on the site, etc. So if you have protectable content that you (as opposed to your users) create, you will want to consider marking those as copyrighted. Also, know that your copyright attaches to your work as soon as it's "fixed in a tangible medium of expression," even if you don't register the copyright, although you would need that registration if you ever had to sue to enforce your copyright.
Additionally, if this is a social network, you'll need to give some thought as to how to protect your users and, equally important, yourself from suits by your users, who might be upset if third parties misuse what the users have posted. You'll need to give some good thought to this both from the technical side and from the legal side. One of the things I believe Facebook does, e.g., is to make sure that everyone who is a user grants them an unlimited license to display any photo they post, and the license lasts for whatever length of time that photo remains up on Facebook--not just for however long the posting user keeps it up, but for however long ANYONE keeps it up on Facebook. Lots of things to think through here vis a vis privacy and copyright.
Trademark:
Also, assuming you are using your site name or a logo (or both) as a brand for your social network service, you'll want to look into trademark protection. The first step in that, however, is checking to make sure the name and/or logo you've chosen doesn't infringe on anyone else's name or logo. Just because you're cleared for a domain name (or for a business name with your state, for that matter), does NOT mean you're free to use that name in a way that works as a trademark. If someone else already has similar mark, your use could be infringing even if you've paid for the domain and have your business name registered.
The standard for infringement is "likelihood of confusion", the idea being that you shouldn't be confusing customers into thinking your service comes from some other business with a similar name or logo, or that you're somehow associated with the other business. (Similarly, from the business perspective, you shouldn't be profiting off the good will someone else has developed in the trademark for their business by bringing in their customers who confuse you for them.) When choosing a business name or logo, check to ensure you're clear to use it before investing in it--whether that be buying a domain or registering the business with your state or paying an artist to work up your name and logo into a screen display.
And check more than just the registered marks at the PTO, since in the US a trademark exists by virtue of someone using the trademark as a trademark. Google the name along with spelling variations and similar sounding words -- remembering that the standard is that there be any "likelihood of confusion," not that the marks be identical.
When you have a name that you believe is clear, depending on how much money you have and are planning to invest in the site, you will probably want to get your conclusion confirmed by having a trademark attorney do an analysis of the mark, bringing to bear his or her experience with how courts have interpreted "confusion". But doing your own investigation first, will help. Note that the attorney will not likely give you a definitive yes or no as to whether the mark is clear since these things are a matter of judgment on a sliding scale. (If the attorney is discouraging you, however, take the hint.) If the way does seem clear for your proposed mark, and you can afford it, you may want the additional protection of federal registration.
Good luck.