I have the same truck as you, except it has a 350 V8

It's a 97 Silverado 1500 shortbed. Anyhow, I've never driven the 6cylinder version, but mine can smoke the hell out of the tires. All I have to do is give it a little more than 1/4 throttle and they start to spin, even on dry ground, if I'm going 35mph in a straight line and give it full throttle I can break the rear end loose on dry ground. My tires aren't worn badly, they only have 25k miles on them with plenty of tread. In the rain, forget about it, it's nearly impossible not to spin them going around a bumpy corner, or uphill unless I throw on the 4wd. The nice thing is that it's fairly heavy so it doesn't tend to fishtail around corners, you just hear the tire spinning but oversteer doesn't occur.