I've always liked the Mr Clean car wash soap. It seems to strip about anything stubborn off the car after letting it soak for a bit on the car.
A clay bar can really bring some shine back to a car, especially if it hasn't seen regular washing. I detailed an 06 Charger awhile back that had never been washed before. Ever. The owner was having some rough times basically the whole time he owned the car and it never got cleaned. So I started with a good wash...then washed it again. I then clayed it using lots and lots of mothers detail spray. The claybar was done for after use on that car, but it went from looking like matte red paint to high gloss red paint. I then buffed it using Meguiars polish, which really let the paint pop, then waxed it using The Perfect Wax. That car looked like a mirror after it was done.
The clay made the biggest difference in the whole thing. Once all the "gunk" was gone, it looked 100x better. The Perfect Wax isn't the best for making a car shine, it's gotta be shiny first. But it does stay on the car for quite a while. If you're looking for something else to make it pop, the Meguiars NXT 2.0 wax does a great job of that. The downside is it doesn't seem to last quite as long.