How do commercial aircraft stop after landing? Apparently it's a combination of disc brakes, spoilers, and engine thrust reversal.

In extreme circumstances the brakes alone can be used, but this is best avoided. To find out why, take a look at this video of a Boeing 777 performing a "Rejected Take Off" test, stopping from 210mph, fully laden, using the brakes alone:

Result: Carbon brake discs and pads glowing at 3,000ºC, melting the tires, and destroying the wheels. (The success criteria for the test was that the entire plane didn't catch fire!)