Hi Gareth,
I haven't shiny sided any Weinmamn rims before but they can't be too different to most other alloy rims and I've done my share of them.
These are my ways but everyone has their own way of doing things so please don't treat them as gospel.
If you are going to do it by hand:
First, I use wet and dry in about 10 different grit grades starting with 150 grit all the way up to 2500 grit. As your rims are NOS and aren't well worn or damaged, you may be able to miss a few of the courser grades at the beginning. Use it with a sanding block to get the best results. By the time you get to the finest grade your hands will be knackered but your rims should be nice and smooth. Then you could use a fine cutting compound, then finish off with something like Peek.
If you are machine polishing:
I use about 5 different grades of polishing bars from a harsh cut to a very fine one using different mops each time going from hard to soft. If the rims were very badly damaged I'd use a grinding paste on a sisal mop but you won't have that problem. It's easier on the hands and quicker but you should wear gloves, a mask and goggles as the dust gets everywhere. It's also not as easy as it sounds, especially on rims so you might want to practice on something else first. You can get all the polishing equipment from several places online if you Google it and a little goes a long way so the bars last a while so they're pretty good value.
Either way, it's not going to be particularly quick or easy but the end result is even more pleasing knowing that you've done it yourself.
Hope this helps,
Giles
