I agree with what Terryallan said for that vintage of half ton. Stick to under 5k dry and you should be pleased.
I also recommend looking into a GM 6.0L truck from that era. They have a little power power than the 5.4L and 5.3L in the half tons yet use a little less fuel than either from that time. And they come in vehicles that have higher payloads which open you up to say 7k dry TTs.
FWIW, the Avalanche is based on the longer Suburban SUV wheelbase and was also offered in 3/4 ton with 8.1L and over 11k pound of tow rating. It can be a bit more than glorified Tahoe. Payload is low on them, though.