Products like the Turtle Wax you mentioned are just full of coloured fillers that mask the defects in the paint for a short while.
You need to permanently remove them using a polish with a degree of cut and ideally with a rotary or dual action machine. Once you have a good base to work from you can use sealants, glazes and waxes to protect the finish and give the depth of shine you are after.
Many will disagree, but to most people, wax is wax. Yes some will be more durable, some will offer a greater shineyness, but none of them will reach their full potential if the standard of the paint underneath is not up to scratch.