What Kind of Oil and Antifreeze Do I need to use in a 2002 Honda Civic LX?

Motorcraft oil will be fine.

Many car manufacturers say to only use their brand of various fluids. Most of the time that’s overdoing it, and other brands of standard products will work just fine. Sometimes, however, it does make a difference and using a substitute will cause problems. That’s very often the case with later model automatic transmission fluid, and it’s the case with Honda/Acura power steering fluid. Whether it’s the case with Honda antifreeze I don’t know. Zerex (Valvoline) indicates OAT type antifreeze (e.g. Dex-Cool) is appropriate.