There are two good ways to start out.
- Fiber Optic Lapping Film on a dead flat glass or marble plate. (not lapping paper!)
- a Synthetic Stone progression (Norton, Shapton, and Naniwa are good ones to look at)
Either of those will get you started in an inexpensive fashion and will get you killer edges. (In the case of lapping film, those edges can be beyond Feather blade sharp.)
Whatever route you go, a pasted strop will serve you well.
Natural stones are each their own huge rabbit hole, JNats (Japanese Naturals) being the deepest and widest hole of all of them.
Coticule is "a low-grade very-fine-grained metamorphic rock consisting of
spessartine in a matrix of
white mica and +/- submicroscopic quartz." Spessartine is a form of garnet. Coticules are great as a single stone honing solution. Look up tutorials on the "Dilucot" method, which uses a slurry on the stone that is slowly diluted until it is just water. As the slurry gets thinner the edge gets more refined. If you just want a single stone to use and not worry about it, this is a good way to go. Coticules have apparently been used for honing for centuries.
Arkansas stones are Novaculite which occurs naturally in the Ouachita Mountains of central Arkansas. It is a dense, hard rock that has been mined for whetstones since around 1818. The stone varies in density from which you get the different classifications of stone, i.e. soft, hard, etc. "Translucent Hard" and "Surgical Black Hard" stones are the two most dense and are frequently used as finishing/polishing stones for straight razors. Less dense stones (Soft and Hard) are popular in the US for honing knives. If you want to know more about these stones, there are two "101" articles on Dan's Whetstones web site. If you want to use only Arkansas stones, you will probably need to have some sort of progression. Also, Arkansas stones can be a royal pain to lap (i.e. flatten).
I recommend staying away from JNat unless you are independently wealthy. Those can take lots of time and expense to find the right stones for you. They do, however, produce amazing results.
All natural stones take time and effort to "learn the stone" due to naturally occurring variations between each stone, even within the same type. No two Coticules will behave exactly the same, for example.
Any of these methods can produce a smooth, shaveable, comfortable edge. It is more a matter of what appeals to you as a way to get those edges. Choice of honing setup is completely personal preference. For example, I hated using lapping film. I tried it on two razors and was done because the film kept pulling up from the backing stone which led to me cutting the film and having to repeat work. However, there are some people for whom lapping film is the best thing ever. It will take some time and effort to find a setup that gets you the edges you want with the maximum amount of time, effort, and money that you are willing to expend in the process.
That being said, so far I get the most enjoyment from Coticules and Arkansas stones.