Episode three (counting the first, double-length episode as two) is The Enemy Within. A few important things get established this episode, the first being the "iris", the metal shield they put over the Stargate to prevent the Goa'uld from just walking into their base any time they feel like it. There's some technobabble explanation, but that's not really important, it's just a door.
One thing that stood out to me though, and I don't know if this continues and I just forgot, or if they drop it eventually, but the whole base goes into self-destruct whenever anyone unauthorised tries to get through the gate. They have to cancel the self-destruct when the wormhole closes. This on top of the guys with guns pointed at the gate and the iris itself. It seems like overkill.
Next up we have the issue of Teal'c, who the US government quite rightly regards with suspicion. Jack is, of course, vehement that Teal'c be trusted implicitly, while Hammond makes the very reasonable point that he was very recently working for the enemy and may be a spy. And really the only reason the audience agrees with Jack is because he's the protagonist. But of course we know he's going to get his way and Teal'c will be part of SG-1 going forward.
Next we discover that Kawalaski is a Goa'uld when he kills a doctor. But because it's a baby it doesn't have full control of him (or it wouldn't have let him go to the doctor, presumably). The Goa'uld is also pretty dumb since it makes straight for the gate to go home and is, obviously, stopped.
Kawalski continues to switch back and forth between himself and the Goa'uld while the rest of the team try to figure out what to do about the situation. Along the way, he takes Sam hostage, because of course that happens. Not Daniel or one of the other civilians, it's got to be the woman.
Anyway, they recapture him and decide to cut the Goa'uld out. This is considered a highly risky operation, and the higher-ups want to let it take over him and keep it prisoner so they can question it, but obviously that would be evil so Hammond calls up his BFF the president and gets authorisation to try the operation. We also learn a few Goa'uld fun facts from Teal'c, like how they're born knowing everything their progenitors knew, and about the whole Goa'uld/Jaffa relationship.
Long story short, turns out the Goa'uld has transferred its consciousness from its own body to Kawalski's, so cutting it out does nothing, and they end up having to kill him anyway - which Jack does by sticking his head into an active Stargate and then turning it off. It's pretty cool but also pretty dumb.
Over all, this episode is kind of important, because it does continue to establish the basic premises of the show, but it's also not a good episode. We know that there are more worlds out there to explore and a bad guy who wants to invade, but instead of that we just get a weak side-plot set entirely on Earth. The baby Goa'uld was there by accident and other than the death of a character we haven't had time to even start to care about, nothing of consequence happens. It's a really slow start.