To keep that texture you can strip the rust chemically. You can use naval jelly or bluing stripper to remove the rust. I would leave the pits as part of the texture. Then dip it in baking soda solution to neutralize the acids. Then rinse it clean.

At that point the rust would be gone and you would be back to a neutral steel surface. It would probably be a good idea to coat it with WD-40 and let it set overnight to make sure and pull any moisture away from the surface of the steel. Should be ready to go at that point.

Sometimes the acids in the rust/bluing strippers can turn the rust black as it neutralizes it. If that happens you can dip it in paint prep acid to take it back to white. If you like the darker antiqued color you can dip it in ferric chloride and that will leave a darker finish. Then you an burnish or lightly sand off he surface and get an antiqued sort of look to the whole area and camouflage in the pits so they can't be noticed.

Ray