For larger line such as parachute chord I default to a Bowline Knot. I prefer the more secure version that I learned from a commercial diver where the line loops around the 'main' line twice (repeat steps 5 & 6 so there are two wraps before going back through the loop to end the knot).
For smaller line, such as 50# braided Dacron fishing line, I will use a San Diego Jam Knot. I prefer this type of line for rigging small latex weather balloons because it is much lighter than the standard 550# parachute cord, is easy to work with, and doesn't have a bending issue like Dyneema/Spectra. But it does require a knot or splice that won't slip loose.
Carabiners: If you use one, please make sure it is a locking one. I've seen numerous failures from ones like the two black non-locking carabiners pictured above. Small line can easily open those and come loose.