It's hard to tell what your paint finish
looks like but let me at least address the
feel of it.
(First, always
wash a car before waxing, claying or polishing so you are not rubbing dirt dust or contaminents into the surface.)
To maximize the results of any wax job you should
clay the vehicle first to remove embedded contaminents in the paint.
Claying is a very simple process that will take less than 30 minutes for a MINI and will leave the surface SOOOO ultra slick and smooth. If you wax over a dirty
bumpy surface...you still have a dirty bumpy surface! Yuck. Check out the article. You don't have to do it that often but it is worth the results. Trust me. (If your paint has no swirls you can go straight to waxing)
Polishing, in the process of paint finish prep, is the next step. This is needed if you have mars or
swirls in the paint that need to be removed. Technically, polish is an abrasive and/or solvent that cleans the surface of the paint/clearcoat. There are many different chemical combinations of polishes and each do their job to a different degree with a different level of effectiveness. Many cheaper "one step does it all" cleaner waxes have a high level of cleaners and abrasives in them to help remove and hide light swirls while you wax. These waxes really are polishes. Often, if you ad another coat you are simple removing the previous coat, not "adding" another on top.
A true wax is just a coating and has little or no abrasives in it. There are two main types of waxes.
Carnauba based which are "natural" waxes and are high solvent based waxes. These are generally easy to use, but have low durability. They will start to dissipate in a matter of weeks. The other type,
sealants come in two categories, Polymer Sealants and Acrylic Sealants. Sealants are far more durable. Some brands can last many months.
Waxing is always last. If you use a polish after you put on any coating you will simply remove it.
There are lots of good
articles to check out. I have only spoken in broad generalities. Look em over! Have fun. Ask questions! You'll be hooked!
Brad