The chain idea is good, just depends on how it is attached.
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I usually buy climbing rope of various diameters on 'the bay". Also have gotten various 'small stuff' ropes, down to 1mm diameter. You can find new and used rope, though I wouldn't buy used rope for actually climbing.
If you look for the shorter lengths, 25-30 foot or less, it is usually reasonable in price. That short of a length is usually too short for climbing uses.
I just look at the brand, google it and decide if it is good enough.
Just get a ruff idea of the diamter you need and look about. Sooner or later a deal comes along - the rock climbing fad resulted in a fair amount of good used rope and accessories.
For a punching bag, you probably don't want static ropes as a little spring to the rope might be desireable. Look at the ropes abrasion resistance, too, as I'd think you'd want a 'high' in that area, too.
Spectra is expensive - do they even make rope with it anymore - but Spectra is pretty strong stuff.