Given the choice between hot or cold rolled I think I would go with the hot. For one; I find it turns a little more predictably than cold rolled which can have hard zones right next to soft spots and two; cold rolled can have a real tendency to warp if you remove more metal from one side than the other. Might make for a nightmare trying to true the face.
If you’re worried about the mill scale, an hour or so in muriatic acid takes care of that nicely. Just do it outside and not near any tools or machines you care about. Supposedly vinegar works too, just slower.
Let's add to that. Muriatic - that is the industrial version of hydrochloric. It is swimming pool pH adjustment acid, and it is very aggressive.
The advantage of going at a metal with any acid is it works reasonably fast, and is handy, and cheap, with easily purchased ingredients. compared to "gentler" more expensive ways like chellation with EvapoRust. Other rust removal acids are phosphoric acid (like Coca-Cola), and citric acid.
BUT... the instant you wash it off, and let the air oxygen see the chemically exposed iron, it will flash-rust right before your eyes, and worse if you used a steam-cleaner. Even after oiling, there seems no way to make it permanently quit. The answer is to de-activate the iron, done quite easily by keeping it wet until you can douse it in something to neutralize it, and then go further, and try to get some hot alkali on it.
Try dissolve a few tablespoons of washing soda, or even caustic soda (carefully !), heat the water some, and leave for maybe an hour. It cools, and then, with some oil after, will have calmed down the raging rust activity.
Even rubbing some wet baking soda over the part can bring the flash rust effect to a stop. Going all the way, and deliberately converting a flash-rust coat to magnetite, and then oil it up, is, I understand, even more effective, but those "conversion" fluids that go purple, and stain your skin, and clothes, are expensive!. The guys who do surface treatment for their guns will know lots more about the ways of deacivating the iron. When I saw it happen, on my lathe bed before I painted it, I was amazed how it could turn orange in only 5 minutes or so.