Since the car is stock, take the code at face value and look into #3 ignition. I'd first see if you can get the problem to "switch" cylinders by swapping the coil for 3 with another. You need plugs anyway, so replace them and take a close look at them all, see what they've got on them as far as deposits go etc. When you're looking at the coil "cover" bit, check for cracks or weird discolourations.
With any luck it's just a loose connection and/or an aging plug. (Sometimes if the coil pack is lose and it's dark in the motor bay you can see faint arcing -- I mention it as a curiosity, not because I'm suggesting anyone put their face as close as possible etc -- be careful, there are real potential differences in the ignition).
None of this is fun to do but grin and bear it and hopefully it'll be a simple "aha!" fix.