Polish exterior chrome on my auto

A. That 40 year old chrome was only about 30 millionths of in inch thick when it was new. I wouldn't buff it with anything grittier than chrome polish and a very soft buff, and wouldn't have any confidence in success. Sending the chrome to a plating shop for replating might be a better idea I think.

A. I've been told that Coca-Cola and aluminum foil work very well (better than supposed chrome polishes).

A. Sounds like a nice car. Spend some money on it. You stand a greater risk damaging the parts if you are not experienced. There may be some small stainless steel parts you may be able to buff out to a nice shine as long as you don't tangle them and yourself in the buff and sustain injury to you and damage to the part. But The little hobby buffing wheels you're talking about will not be able to get any scratches or nicks out.
Take you parts to a good reputable custom chrome plater.
The bitterness of a bad job will linger much longer than the payment of a good job.

Good luck,

A. The aluminum foil and coke trick works, but not as well as a real polish, here's why.

Most soft drinks (colas and the like) contain carbonic acid in small amounts, this throws the pH slightly to the acidic and enough to eat away at rust (de-bonding the oxygen from the metal).
The amount of acid in a can of coke is negligible, you can't dissolve nails, meat, or anything else of substance with coke.
The use of aluminum foil is pretty much like using very rough steel wool, the problem is that you will likely scratch up the surface you're trying to polish pretty badly and have to polish it afterwards.
Normal polishes are more on the level of a mild abrasive and a mild solvent. Brasso [on eBay or Amazon] is a great example of this and works like a charm for most polishing needs, if you need to do something beyond polishing I would suggest using sandpaper, starting from a very rough and graduating to finer and finer until reaching something around 800-1000 grit sandpaper. Then going in with either a buffing, or polishing compound.