I have been using Permatex 403D for twenty five years on both full-size and model planes. It's used largely by the aviation industry to clean/polish windscreens and canopies.

It has a consistancy of skin lotion and won't scratch a dirty windshield (if done properly). So no need to clean with anything first, just use a liberal amount on a dirty canopy and it will lift dirt away and polish at the same time.

To polish your canopy, use an old (soft) clean cotton sock (use wet to clean and dry to polish) and polish in one direction (same as airflow - front to back,etc) not in circles.
Never use windex or anything with amonia on clear plastic or plexi-glass. It will scratch.
Another property of 403D is it will rejuvenate old dry plastic and plexi if used often.

Yes it works on your car's Lexan / plexi headlamps. It takes only ten minutes each light and twice a year to keep my '97 looking like new and what a difference driving at night.

You can buy it at any pilot supply and I think Aircraft Spruce even sells it. Of course it's available at most auto parts stores as well.