What’s best kit or single tool for pulling packings ?

Palmetto makes a whole lot for around $100, or you can just use drywall screws and a pair of pliers

Texacone sell packing kits.

I've used a screw and vise grips before one on the was real stuck. But 99% of the time a good set of picks does the job. If I remember correctly I got my set at an auto parts store. The one that's bent at a 90 degree is most handy. They're also worth having when replacing o rings or seals in valves and getting out them tiny parts.