The frogs are cute, just be sure like the others said you don't end up with the clawed frogs. Often petstores mislabel them, or mix the two up, sometimes even putting them in the same tank and labeling them all the same thing. So if you decide to go the frog route, do some searches online for some pics of "African dwarf frog" and "African clawed frog" so that you can tell them apart.
Adding new fish a little at a time is a very good thing to do. Though, I might suggest you consider adding the bottom-feeders earlier, as they are great at cleaning up any leftover fish food that makes it to the substrate...which in turn helps you maintain good water quality.
Your hatchet will definitely be happier with some others, they are essentially schooling fish (at least in the loose sense of the term.)
I don't want to discourage you from cardinals, but just be aware they have a bit of a reputation for being very sensitive, fragile, and hard to keep alive. If you do a search on these forums for "cardinal" you'll find some posts with people sharing their stories. A heavily planted tank helps, and I'm pretty sure they prefer slightly acidic water conditions (especially water with tannins from natural driftwood), but even still they can be sensitive. Just a warning that they are not the easiest fish to keep, especially in a relatively "new" tank.