Has it ever been stated (by someone in the cast or crew) why Apophis was chosen to be the main villain in the beginning of Stargate SG-1? I am looking for an explanation why Apophis and not another egyptian/other culture god.
From the first episode (or second, if you watch double episodes split-up), when SG-1 is in jail, Daniel Jackson just about confirms this.
Carter: So Ra isn't dead after all.
Jackson: No, it wasn't Ra. It was Apophis.
Jackson: Ehm, it's from Egyptian mythology. Ra was the sun god who ruled the day. Apophis was the serpent god, Ra's rival who ruled the night. It's right out of the book of the dead. They're living it.
Note: what's referred to as the 'book of the dead' is more commonly known as the 'Book(s) of the Netherworld'.
What's a bigger difference than that between night and day?
Throughout the Stargate series, there's a focus on allies and rivals. Who to trust, who not to. When your allies start behaving suspiciously, it's probably because your rival is messing with them (spoiler: Tholans). When you're down, your enemy will show up to make it worse (fighting the Go'auld? Have some replicators). It makes for easy writing, easy following and is probably a trope of some kind.
They kill one of the mightier System Lords so naturally, his rival (who's also his brother) shows up. A few episodes later, his mate Hathor shows up. The show tells us a bit about all the rivalry between the System Lords, but for those interested there's also the Stargate SG-1: Living Gods: Stargate System Lords roleplaying game.
Let's phrase it like this: who was the most logical of his rivals to show up when Ra got blown to pieces? His worst rival. Ra had multiple rivals of sorts, most of them got featured one way or another and only one of them can be first, but Apophis was both in- and out-of-universe his most prominent one. Apophis was the god of chaos, darkness, the anti-light (thus anti-Ra, god of the sun).
When thinking about the underworld, most people think of Osiris. But Osiris is actually Aus-Ra, the rebirth of Ra. Or, according to other stories, Ra merged with Osiris when he entered the afterlife. Apophis is the snake hunting for Ra but never succeeding.
"The essential leitmotif is the journey of the sun-god through the 12 hours of the night, defeating Apophis the snake-god of chaos and emerging unscathed on the eastern horizon at dawn."
They're arch enemies. Taking what used to be Ra's would be the logical thing to attempt for Apophis.
For those interested: for more out-of-universe information on the topic I can highly recommend George Hart's 'A dictionary of Egyptian gods and goddesses' (also known as 'The Routhledge dictionary of', linked earlier in this answer). Considering the intricacies of the out-of-universe Egyptian deities are much more complex than how they're portrayed in Stargate, I don't know how much sense it makes to dig into that for this specific question.