Thanks for asking, I would always, always, always try calling first and follow up with an email. Go through the calling employers video for a script of what to say, but call first.
Connecting on LinkedIn is good, but you want to be careful there, definitely use a personalized message explaining why you’re connecting. I would never recommend connecting on Facebook, that search string process is to find names and leads, not to connect.
And yes, always try to bypass the receptionist and HR. They have been trained to screen you out, whereas everyone else has been trained to help you. So go around if you can.