Welcome to TFF.
Several things to mention here, so...
First, water parameters. In very general terms, there is soft water (very low in dissolved minerals like calcium and magnesium), and harder water (higher level of these dissolved minerals). Some fish prefer one or the other, some absolutely need one or the other, so it is best to sort out your source water parameters so you can acquire fish species that will be "at home" in your water. The GH (general or total hardness) and pH are the two most important parameters, and you should be able to ascertain these from your water authority if you are on municipal water. Check their website. A test for pH is worth having, so this you can test yourself if you have a reliable pH test kit. When testing tap water for pH, you need to out-gas any CO2 by letting it sit 24 hours, or very briskly shaking it before testing.
Soft water fish include most of the tetras, though some manage in moderately hard water, provided it is not extreme. Livebearers like platy need moderately hard water, and they will not do well in soft water long term. So we can sort this out once we know the parameters.
Second thing is about shoaling fish. This refers to a species of fish which lives in usually large groups of hundreds, and the fish has an inherent need for a group of its own species. Tank size often limits the numbers, and it is sometimes difficult to come up with a minimum, but it is important to keep in mind that in most species that are shoaling, having more rather than fewer will inevitably mean healthier fish. So numbers of each species are extremely important. All tetra are shoaling fish. Six cardinals and six rosy tetra is OK, this is about the minimum. If you decide on Black Phantom, they must have at least six, but this is a species that is better with a few more, so I would say 7-8. Male and female are easy to identify with this species, and 4 males to 3 or 4 females would be ideal.
A 200 liter (roughly 50 gallon) tank will work fine for fish like those mentioned, and give you the space to increase the groups for the fishes' benefit.
Personaly I would not mix cardinal and neon tetra, solely from an aesthetic aspect. The cardinals are more col;ourful, and together the neons can appear quite "plain." Increasing the cardinals would be a better option. But let's get the parameters sorted first.
Byron.