Clean heavily rusted structural steel
None of the above?

It's structural steel, you can just leave it rusty (if it happens to be corten, the rust actually keeps it from rusting further...) This may lack Wife Approval Factor for your backyard BBQ, however.

Least marking (and least direct effort, dust, noise) electrolytic rust removal - submerge it in a tub of water, outside, with sodium carbonate (washing soda) mixed in. Connect a low-voltage DC supply to the thing you want the rust off of, and a sacraficial electrode. Polarity is - to the thing you are derusting, + to the thing you are sacrificing. Both should be in the tub, but they should not touch. Turn on the power, let it bubble (that's hydrogen, which is why you do this OUTSIDE, only, not inside.) 

For mechanical rust removal when looking for effectiveness/speed rather than "least marking" I use a knotted wire brush in an angle grinder. Conditioning disks will probably mark a bit less and definitely work slower, IME.