Alright, managed to get email sending figured out, partially. I used Gmail's SMTP server for testing, but couldn't figure out why my configuration didn't work.
Turns out, there's a small setting at the bottom of Google's security page for allowing insecure apps to login, and it was off. Turning it on allowed for my GNU social server to send out emails. The second issue was that I can't seem to use SSL via port 465 on Gmail, but can use 587. Not sure what to do on that though, or if it's a huge concern.
My next step is to figure out how to be able to send the emails out from my own server instead. I'm not too knowledgeable in this area, but from what I read, I would need a mail transport agent? Would postfix be enough? Does postfix work as a SMTP server, and could GNU social work with it? !selfhost