Probably the best thing for you to do right now is to get your hands on a book or two and find out which method works the best for you. Other than the methods you've mentioned, you can also add syrup to carbonated water. In my opinion that's probably the quickest, and least investment. Just grab a bottle of club soda or seltzer water and have at it. I have a list of books here that may be of interest to you. You can pick them up from amazon, or you can probably pick up one or two from the library.
As far as your flavor, I think that the best cola recipes that I've tried are either the one from the 7/5/11 NYTimes article or from the Open Cola project. In my experience Kola nut doesn't have much flavor on its own. I believe it can be a source of caffeine, but you'd be better off getting a USP caffeine powder somewhere online as a more consistent and workable source..
For your sweetener, I don't have much experience with monk fruit or stevia, but you certainly can use them for your soda. There's nothing wrong with tailoring the recipe to your tastes, and that's the best way to learn anyway. Start out at low levels and add a little at a time until it's at the level you want.
Fermenting isn't out of the question either. My local wine supply store sells homebrew root beer kits where stevia is the main sweetener and you only add enough sugar for carbonation. Just use the same guidelines you would to bottle condition a beer, but shoot for 3 to 4 volumes of carbonation. The sugar will be consumed by the yeast, and when it runs out you'll still have the sweetness from the stevia or monk fruit, so no worrying about exploding bottles.
Good Luck to you!