Generally, for a 2003 Silverado 4.8L, 5W-30 is a common and often recommended viscosity, especially in moderate climates. However, 10W-30 might be suitable in warmer climates. Always check your owner's manual for the manufacturer's specific recommendation.
Beyond viscosity, the oil type is a matter of preference and budget. Conventional oil is the least expensive, synthetic blend offers a balance of price and performance, and full synthetic is the most expensive but offers the best protection and longevity. Again, your owner's manual may offer guidance on oil type, but using any of these three types is typically acceptable.
Before you change your oil, always double-check your owner's manual for the most accurate and up-to-date information. The manual will provide the definitive answer for your specific vehicle.