I would have to agree with BSI and Gary Barzel when they say that it depends on the business that you run. Can you give us a little bit more information on your product/service?
But it also depends on what you want from the social networking in
general. Your goal should help you decide.
Facebook is HUGE and, of all the sites you mentioned, it is by far the most social. It also has the biggest variety of demoographics using it - it seems most people have a Facebook account these days. Although that doesn't mean that everyone on there will want to engage with your business.
If your goal is brand building and getting to know your fans and really engaging with them (and letting them get to know you and your business), then Facebook is for you.
Twitter is not so much a social network, as more of a information sharing site. You can definitely build up relationships on it, but unless there is a common interest this tends to be fleeting.
If you have a lot to share and want to learn more about your industry then give Twitter a go.
LinkedIn is a much more professional site, but don't let that put you off. You can make some great connections and even find potential employees (depending on your business).
With all of these sites, what you get out of them all comes down to how much effort you put in. And remember that all these types of sites are a two-way street: don't just broadcast, engage and share.
The best thing to remember before you go jumping in however, is to have a plan: What do you want out of social media and social networking?
If you need help with this then let me know.