When you're writing conflict-driven fiction -- which is most Western fiction, honestly -- choosing an antagonist is pretty important. The actions of the antagonist drive not only the plot but also the necessary arc and change in your protagonist. So that's what we're talking about this week on SFF Seven: picking the antagonist that's going to make things hard for your poor protagonist.
I tend to start thinking about stories by coming up with a push-pull struggle for a character or a relationship, then I populate that struggle with characters who deserve it. (All authors are cruel this way. It's what feeds us.) Somewhere within that early thinking-about-it-ness, an antagonist usually emerges sort of organically. For instance, you know that all good protagonists need to have a GMC (goal, motivation, and conflict), right? The way I keep it straight in my head is the pithy:
What does she want? (goal)
Why does she want it? (motivation)
What's keeping her from getting it? (conflict)
That third thing, the conflicty thing, is the antagonist ... presto! That's how I pick my antagonist.
Note that an antagonist does not have to be a villain. It can be, but it can also be an alien invasion, a volcano explosion, a phobia, a busybody matchmaker, or overdemanding parents who want my girl to be a doctor waaaay too much and won't pay for art school.
If you're thinking in acts, specifically a five-act structure (1. exposition, 2. rising action, 3. climax. 4. falling action or digging deep and overcoming, and 5. denouement), I've heard that Act 3 is All About the Antagonist. Which would make sense, right? Just as the protag hits the brick wall of the climax, that's the perfect time to the antagonist to whip back the curtain, announce its fiendish presence, and make things really super difficult for my girl.
But the dirty secret is that the antagonist has been there all along, cooking up obstacles from the very beginning. The third-act climax is just an opportunity to cue the mustache-twirling and bwahaha.
Okay, I'm not sure if this all answers the "how do I pick an antagonist that will complement my protagonist?" question, but it's the best I can do:
Pick the antagonist that is gonna make things as tough as possible for your longsuffering protagonist, get them working at their nefariousness early and often, and have them really bring the hammer to your excruciating but compelling climax.