For connecting balloon, payload and parachute together, folks from Edge of Space Science recommend braided Dacron line:

Braided Dacron line

HAB-1 payload was very light. This Kaymont 600g balloon, the smallest weather balloon I could find, propelled my creation into space:

Kaymont 600g balloon

And Rocketman 4′ parachute safely descended the payload back to Earth:

Rocketman parachute