In the missions I've played, you don't seem to be able to bring your boffs along with you, just generic security. Is this the way it's set up for now, or did I do something wrong in my mission?

There is a bug, I think, that makes it where players can't pick their away team, but it's not consistent. In most missions, you can choose which BOs to bring. Since your test character is lvl 1 though, you really only have a security team.