Use email addresses. They're easy to get access to, and you'll be able to track open and click activity via applications like Yesware. There are all sorts of toolchains set up to help you with emailing in mass, lead scoring based on email engagement activity, etc.
So Facebook messaging might be cute, but it's not scalable, and not well tooled. Just find their email addresses.
Just spend the time to find the email addresses, or use an oDesker / etc. to do so to help you.
That said, messaging / LinkedIn connections can be helpful. If you are doing a good job of ONLY approaching prospects to whom your offering REALLY makes sense, they may be open to connecting to you and you can deliver a customized marketing message in that invite. This is generally more accepted when you're engaging with Sales and Recruiting prospects. VPs of Engineering and CTOs will typically look down on this.
Twitter, too can be helpful, but less from a spammy "Hey, look at me! Look at me!" but instead following prospects, and engaging with what they say - as in, really responding to them, in a non-douchey fashion. This will raise email response rates. They will likely click through to your twitter profile, where you likely have your company's website / twitter handle merchandised for clickthrough.
But generally speaking, get their email address, HQ phone number, and direct number if possible. Other vectors are not as impactful or scalable, and can be fraught with cultural issues.
Welcome to prospecting. Don't be cute. Think about scale.