The manual will specify the viscosity (like 5W-30, 10W-30, etc.) and the type of oil (conventional, synthetic blend, or full synthetic). Ignoring the recommendations in your owner's manual can damage your engine.
Once you find the specifications in your owner's manual, you can then choose a brand of oil that meets those specifications. Many reputable brands are available, including but not limited to Mobil 1, Castrol, Valvoline, Pennzoil, etc.