I have been making a career lately out of removing rust, as I am restoring my 1965 Schwinn Breeze. I have read LOTS online about what to use, what not to use, what works, what doesn't. Everyone has their opinions, and here are mine! There is a product called LA's Totally Awesome Cleaner that you can get at Dollar General (around here) that works like a charm with 0000 steel wool. It comes in a spray bottle (a bit diluted, I think), or a 64oz bottle concentrate for about $3.50. For rust removal it says to dilute with water 2:1. I was using it, then read online that others knew about it and approved of it as well.
White vinegar works extremely well with 0000 steel wool, too. BUT, be sure to rinse with a baking soda/water bath to neutralize the vinegar or it will leave a funny looking finish...I found out the hard way.
Now about Scotch Brite and Chore Boy pads....They are wonderful little pads for just about everything, but NOT bike chrome. I found THIS out the hard way too. I was using steel wool with success, then read people rave about Scotch Brite and I thought "Duh, I should try that!" It works, all right, but totally dulled the shine of the chrome. Some places are even gray and "flat" looking. I'm really disappointed in that, and now have to decide if I want to re-chrome them. (That's another story.) Here is what Greenephantom.com says about it:
"The ultimate goal in cleaning the chrome is to remove the rust without scratching the chrome. If you use a coarse steel wool, or a Chore Boy pad, or similar, then you will scratch and dull the chrome." I found and read that too late. It didn't scratch it, but it sure is dull. Don't make the same mistake.
So, I'm sticking to 0000 steel wool, Awesome Cleaner, and/or white vinegar followed by baking soda/water. I hope I've helped someone out today!
P.S. And I hope I don't get in trouble quoting another website. I DID give them credit...