Q: Apple G3

Polishing plastic is a very labor-intensive job, but if that's what you have your heart set on doing look for a quality plastic restoration kit. Products used for aircraft window restoration would be appropriate.

I would disassemble everything so that you can immerse the plastic case all by itself into a tub or similar area so that you can wash it with running water. You will need lots of water, sandpaper, polish, and time. Don't dry sand anything unless you want to generate enormous quantities of dust, which is the last thing you would want in its interior (another reason for removing all its interior components).

Another option are those kits sold at automotive supply outlets that restore yellowed and dull plastic headlamp covers. They might be a cheaper option as anything that has "aviation" or "aircraft" in the name usually gets a big price bump.

Test on a section of the case that is out of sight. I would create a small test section on the case bottom, apply the cleaner per instructions, and then wait a couple of weeks to see if any yellowing or crazing has occurred.

There are some likely source links in this dedicated search result.

https://www.google.com/#q=plastic+clean+polish+powermac+imac+g3+plastic

A fair time ago, I knew a lady who ran an Apple repair business and

she used some common items to clean the white and colored plastic

cases of early non-beige 'white + colors' iMac, iBook, & PowerMac.

And surprisingly like new. They brought a higher price, too.

Not sure if she used 'bon ami' or some other cleaner with mild abrasive.

This product uses a 'abrasive powder feldspar' with mild detergent to polish.

For more info on this product and rumors about its use, may be found here:

https://www.google.com/#q=bon+ami+polish+plastic

{The 'magic eraser' items sold in stores may be worth experimentation.

A generic off-brand I bought, has not been tried. Suggests damp use.}

In the links within search are some ideas; commercial plastic cleaners for

computers are available from vendors. And screens can be a specialty.

NewerTech® : iDevice : Clean & Polish Kit

NewerTech Clean and Polish Kit removes scratches from your Apple iPod, iBook,

MacBook (white) or any plastic ... Remove scratches from your Apple iPod, iBook,

MacBook (White) or any plastic surface with this 3 step plastic polish system. ...

Cleaning your Apple products - Apple Support

Since the iMac G3 has a durable cover over the CRT, unlike later iMacG4

with LCD (soft) there are more items that could help clean or polish G3.

Good luck!