Just sanding a chrome bumper to paint it is probably going to guarantee that it'll rust in the typical rust pits that chrome gets. If I were to paint a previously chromed bumper, I'd soak it in rust removal (like evaporust) then sandblast. It would be best to grind ALL the chrome off, as the rust also creeps underneath. I had a previously painted front bumper powder coated, and when I asked the coater about it, he asked if it had been chromed previously. I'm thinking he would have bumped up the price to strip the chrome off. I used a "chrome-like" color and it looks OK, but not truly like chrome. I also have some chrome vinyl wrap that I may experiment with.
Running boards do take a beating. I used bedliner on mine.