I clean rusty machine parts the same way i would to pre-pair a steel panel for paint .
1) mechanical clean using wire brushes( hand of power ) ,scourer pads etc and don't push to hard on the wire brush if it a powered unit as you will gall the surface .
2) Degrease using thinners or similar and let it dry .
3) De-oxidize using a rust converter (phosphoric acid type ) this can be purchased at auto parts stores etc – keep the solution fairly weak and wear your PPE !
4) Wipe off with 2 wet rags , one is to take the bulk of the acid off the second to clean off any residue and neutralise it .
5) Immediately rinse with Methylated spirits to pick up the moisture ( it absorbs water ).
You would then allow it to dry and oil it .
The rust converter will kill the rust left in the pits on the surface that mechanical cleaning won't remove and NO IT WILL NOT EAT THE PARENT MATERIAL AS LONG AS IT IS STEEL OR CAST IRON !
If you want a shiny appearance then polish with a scotchbrite wheel (green type similar to a buffing mop) mounted on a bench grinder of power drill.