I use a product recommended by a member here. It's a metal polish that was concocted for use in restoring an old DC3 aircraft that was heavily oxidized. Takes lots of effort to polish an entire DC-3!
The company that sells this Met-all polish is Aircraft Spruce.
If I run out of Met-all ( which also works on chrome and stainless) next best thing is Mother's Aluminium polish.
I have Autosol in the drawer but only use it in extreme situations, such as removing blueing from chrome exhaust pipes, something I'm doing less and less of over the years. In my view, Solvol is pretty harsh stuff . It will remove the blue but always removes some shine as well.
Solvol is also a bit pricey, as is Mother's. The Aircraft Spruce product is cheap stuff, $30 CDN for a 2 lb can. If you do a lot of polishing the big can is nice, saves running to the store for more. In this case I've found the cheapest stuff to be the best product.
Thanks to the member who recommended it to me!
If the rims are really heavily oxidized, then yes it is faster to get out the buffing wheels and buffing compounds, starting with the finest compound that will work to cut sufficiently fast. In other words, do not start with a really coarse compound unless you have to. It takes a lot of work to get the coarse scratches out, but sometimes there is heavy pitting etc and coarse compound must be used.
Work from coarse to fine. Once it is polished, the Met-all or any other alloy polish will work for maintenance of the shine.
Glen