Years ago, when you'd go to a car show you'd see the detailers with a tube of something wrapped in tape and they'd be using it to rub out minor scratches and scuffs that got on the cars during shipping and set up.
The method was this: Using a soft cloth, t-shirt material or diaper they'd put just a little of that material on the cloth and rub on the scratch till it went away. More pressure to begin, less and less till it was finished. Then, they'd wipe it off and check. If it was good, they'd wax over that area.
The material in the tube then and my recommendation now is - because it's widely available and I doubt from your post that you're interested in buying machines and learning to use them then... - Blue Magic Metal Polish.
It might take you awhile because this is a spot repair method and you have more than just spots but it is safe - read the label, it says use on plastic and paint - and it's as close to beginner proof as I can think of. You'll figure out pretty quickly as you go how much pressure you need to put and what it takes to finish down to the gloss that matches what you've got.
For a top coat/wax I'd suggest any of the better carnauba waxes. Put it on thin, let it dry, wipe it off. Streaking isn't likely to be a problem since the sun probably doesn't shine inside your house.
Take Care,
Robert
