First welcome to the website,
Using stock rims limits the tire size to the size of the rim but there are several rim sizes to choose from even from the factory, ex:
Stock on basic AV may be a 16" rim or on a Z71 AV they came with a 17" rim and I believe some years had 20" rims as an option on first gen AVs (2002-2006).
My 2008 AV Z71 came with 18" rims.
The advantage of using a 17" rim or larger on a first gen AV is that you then could use the larger second gen brakes for better stopping ability.
So without knowing further about what rims you have it is hard to answer your question. Also are you looking for larger diameter tires or wider tires then stock? If the diameter is larger it will affect your odometer and speedometer readings and you will have to get them re-calibrated. If you want wider tires then your gas mileage may suffer some due to more rolling resistance and weight.