First, Kollin, welcome to Tropical Fish Keeping forum.
Second, I certainly agree to forget the Betta. One, a male Betta frequently takes a dislike to other fish and will eat tetra [mine did]. Second, even peaceful tetra will tend to nip the fins of a Betta when the temptation is so high.
Third, to the danio and tetra. I would leave the danio out as they need more room. At this point, I'll refer you to our profiles, under the second tab from the left in the blue bar across the top of the page. If the name is identical in a post to that in the profile, common or scientific, it will shade and form a link you can click to see the profile, example Zebra Danio. The profile explains this is an active fish, so more swimming room is better.
The Black Neon Tetra is OK. But with soft (GH 4 d) acidic (pH 6.5) water, you are in the enviable position of having a wealth of rarer fish suited to your water. And with a 15g, there are some lovely dwarf species that would allow you to have more fish and thus more interest in a relatively small space. For starters, have a look at Hyphessobrycon amandae, Boraras maculatus, Boraras brigittae, most of the species of pencilfish in Nannostomus [any except N. beckfordi], Brevibora dorsiocellata, and perhaps a couple of the anabantids in the gourami group that are miniature. For the substrate, a group of one of the dwarf species in Corydoras. Lots of options.