Twitter will only be good for your business if that's where your target audience hangs out.
If your audience is mostly on Facebook or LinkedIn, then that's where you should be focusing your attention. It's not about Twitter being right or wrong, it's about it being the right place to find your audience.
This is where marketing personas can help a lot.
Come up with the notion of your ideal customer. What are his or her pain points that you can solve? Where does s/he work? Where does s/he live? What does s/he look like? What's his or her name? Really flesh this "person" out so that you almost feel like they're a friend or acquaintance.
Once you come up with a marketing persona and can put yourself in the mind of your target customers, it'll be easier to figure out if Twitter is the right place to reach them.
If it is, then I'd highly recommend HubSpot's "Twitter for Business" kit, featuring videos, eBooks and articles about how to use Twitter effectively for your business. Lots of great stuff.
Disclaimer: I work at HubSpot.