For what someone else might charge you for a full detail, this cost could be put toward a nice DA Polishing Machine. The two most common would be either the Porter Cable 7424XP, (which is what I have) or the Griots Garage GG6.
Pair one of these with a Lake County 5" Backing Plate, a few of each Lake County 5.5" Flat Pads in Orange and White, you're pretty much basically set with the tools.
They are simple to use, relatively safe, meaning you won't burn your paint, or create Hollograms (Buffer Trails)
Many "common" regular run of the mill detail shops rely on tools such as Rotary Polishers, and while in the right hands they can do better correction, and faster correction, remove heavy damage, they can also remove way too much paint, cause Hollograms like crazy, burn paint.
Now yes, there are good detailers all over the country, but just as many bad ones as well. Most car dealers are not exactly the place you want to have your vehicle deailed either.
As most experienced detailers will tell you, there is no way to say in any particular instance what will work best as a polishing product, and there are hundreds out there of various agressivenesses. A general rule of thumb is to use the least aggressive products, techniques, and tools and pads to get the job done.
For the average vehicle owner who wishes to maintain their own vehicles, the DA Polisher is usually ideal and easy enough to use where you will not get into trouble.
Yes, hand polishing is sometimes the only way to get into tight areas, such as around emblems, around door handles, mirrors, bumpers, etc, but hand polishing can be pretty much ineffective, very slow process on large panels, and one will not ever produce the same results that a DA Machine can.
Again, and as for what polishes, and products to use, always use the least aggressive. Many folk's vehicles have scratches so deep that nothing will remove them.
A very high quality, gentle, and ultra fine finishing polish that is usually very easily gotten, produces superb final results, and can be used via hand, DA, or Rotary would be a product such as Meguiars Mirror Glaze 205 Ultra Finishing Polish. This product should be in all detailer's arsenals, it is that good, and it produces beautiful final results. It is easy to work with, even by hand.
This product is one of many available that is perfect for removing light swirls-fine scratches, haze-clouding, minor oxidation, and will produce a very high super glossy luster to paint, whether single stage, or 2-stage base coat/clear coat paints.
Black is of course the hardest of all to maintain. The better you then refine your washing techniques, the less swirls you will instill after paint correction.
The general rule of thumb is wash, clay-decontaminate, polish, seal/wax.