Wax, polymer or ceramic?
 

What's the best thing to use and why?

The most important thing is the prep.

There's way too much info to list here.

If you get a chance, you may want to check the Autopia.org forums. Tons of info and industry professionals who share their knowledge.

As Prange said, prep is the key
I know this is an older post, but when I owned my detail shop in Silicon Valley, Ceramic is the only way to go now. It is a bit more than your off the shelf polymers and waxes, but in the long run well worth the price and effort.
I am a huge fan of Kamikaze products for the hobbyist, or Feynlabs products for a pro installation. I dealt with Ceramic Pro which is very good but it did not make the paint pop like I could do with Zaino products. The advantage to Ceramic Pro is the lifetime warranty.
Feynlabs products made the paint POP!!! Kamikaze was close, but not quite as good as Feynlab.
Now there is a plethora of products out there, and if you see it on FB, run away...

wax definitely