Hello Kaylea,
I suggest to go ahead and get a webcam, they are cheap, and not only your family can see your beautiful baby but you also can see them, and the baby can see them. My webcam has a microphone in it, so I don't have to wear a headset at all, I just sit here and talk. Some webcams don't have the microphone, and you have to wear a headset. I suggest to buy one with a microphone incorporated into it so they can hear the baby as well and you don't have to worry about putting the microphone here or there.
If you choose to only go with a microphone, it is just like talking on the phone, except Skype is free so chances are it would be much cheaper than the phone, for international calls (mind you, Skype does not connect you with emergency services, so don't use it as a substitute for a phone). I would double check on the Skype website to make sure you can have a connection with just a microphone, because I have never tried, but I know that if you have the webcam you can turn the video off and simply do a phone conversation on Skype. So it seems logical to me you could connect just with a microphone, but I am not sure.
For language study it is very very important in my opinion to do regular conversation in the language. It is very different trying to talk or understanding someone who is talking and knowing how to answer, than when you are writing and have time to look things up and think. And the person you are conversing with will help you with the fine explanations and language expressions that in writing simply takes too long to write and you miss all that.
Rich blessings,
Lydia