While you asked a very simple question, it actually requires a pretty complex answer that could forum the basis of a book.
There are two parts two creating the ultimate deep shine: the actual shine of the paint which you control by altering the paint's surface (the prep work); and the layers of waxes, sealants, or glazes you add on top of the paint.
It's all in the prep! Most professional detailers would agree that the 90% or more (I would argue at least 90%) of the shine is in the work. To get the ultimate deep shine the surface of the paint has to made as flat as possible, even at the microscopic level. When is uneven and marred, reflected light actually scatters or refracts, as it is sent in different directions. Taking paint to its highest level and ensuring the sharpest, richest, and clearest gloss requires leveling the paint as much as possible.
If we keep in mind that the smoother the paint is at the microscopic level the greater it will shine, the prep work is a matter of using the right tools to level the paint at this level. Experience is going to be the best teacher in helping you select the best tools and technique to manipulate the paint for the best shine. There is no blanket answer or no set process will give the ultimate shine on all paint systems. There are too many variables, such as skill level, pad type, paint type, paint workability, abrasives, lubricants, humidity, temperature, etc. However there are good recommendations that can get you heading in the right direction.
Most boutique level detailers I know will spend hours and hours and hours polishing the paint once it looks perfect, trying to refine the paint to get the ultimate gloss. A good friend and great detailer once told me he doesn't even start polishing until the defects are removed. Meaning that removing swirl marks and scratches (macroscopic defects) is the easy part for him. It is the hours spent afterwards (when post people would be very happy with the results) trying different final polishes, pads, speeds, machines, and techniques to find what gives the ultimate results to their trained eyes. It should be noted that these detailers are often getting paid big money for their experience in these cases.
So there is no set answer to what final polish and pad gives the best results all of the time. In my finish paint arsenal I have all of Menzerna final polishes, 3M's Ultrafina, Meguiar's M205, M80, M82, and M09, Mark V polishes, and a couple of other brands as well as just about every finish pad there is. For final polishing with a rotary polisher I will usually find that either Menzerna PO85rd or PO87mc and a Lake Country Black pad or 3M's Ultrafine (ultrafina) polishes can achieve phenomenal results on most paint finishes. The rotary polisher will tend to achieve a higher gloss most of the time because it can break down the abrasives more evenly. With a dual action or random orbital polisher I will tend to reach for M205 from Meguiars, as the non-diminishing abrasives will finish equally well regardless of machine.
If you are using a Flex, I would start with Meguiar's M205. If you grab a rotary, 3M's Ultrafina is going to be the most forgiving.
Once the paint is at its fullest potential, the focus achieves on alerting the natural shine of the paint by selecting the combination of products that will not only protect the paint but add shine and gloss. I think Blackfire's Wet Ice over Fire kit does a great job of adding gloss, depth, richness, and wetness to the paint. Alternatively, I also like to select various waxes and sealants besides this for certain situations. Again experience and personal preference are going to precede anything I can tell you.