Just bought an 03 5.3l z71 Silverado, engine drives great, transmission seems to shift but ..

When accelerating quickly from a stop, there's a slight jump to 2nd

When coming to a stop, there's a slight grunt noise right before a complete stop feels like the cause is from it downshifting to 1st.

Seems 1st gear is having an issue?

 

accelerating like a lead-foot or like a granny?

do a "drain and fill" on your trans fluid. If it's really dirty consider doing it twice or doing the next one sooner than later.

make sure you you are not above "full hot" when it's hot. alternatively - if you didn't heat up the trans on the highway before checking level: make sure it's a little below full hot. so it doesn't foam.

> slight jump

what do you mean? it the trans slips? or the trans hits 2nd gear too quickly ?

 

It does feel almost like a slip I asked my friend who has a 2wd 07 owned since new and he say his does the same thing.

So just do a simple fluid change for now and skip the oil filter?