Hi Brandon,
There are so many tips regarding cleaning & polishing; the best one is to use caution.
Not all plastics react favourably to chemicals in household cleaning products. Even then, some which work for others, may not work for you.
E.g. Brasso Metal Polish dissolves expanded-polystyrene (a type of hard plastic). T-Cut can strip the shine from smooth plastic panels. And products containing alcohol (e.g. Windex) can wipe off decals in an instant.
Try to disassemble components first. Photograph as you go. It makes cleaning easier and avoids cleaning product cross-contamination. Mark your cleaning rags.
There's a wide choice of products and polishes on the market now. Most in your auto store. Some especially designed for plastics. They're not cheap, but they're worth it. Try to avoid using whatever's laying around in the shed. Tempting though that is.