[JustOneMore20]

I agree with Ultasol, choose either the platies or the swords. I would go with 2-3f/1-2m. If you like neons, then I think they would be fine with the other fish. I know they have different hardness preferences, but I'm sure you aren't going to be adjusting your water for the livebearers. Most fish can adapt to any hardness.
I personally think there are more interesting tetras out there besides neons. I like lemon tetras, rummynose tetras, and harlequin rasboras (not tetras).

Its obviously up to you what you choose. I think black neons would be a good contrast to some orange platies (if you can find some orange ones). They would also compliment a betta (of any color).

Here's what I would do:

1 betta
3-4 platies
8-10 tetras
6 cories

I agree that danios can be nippy. I wouldn't trust them with a betta (especially in the 10g). I think I would be safe and just not include them in the new tank. For the 10g, harlequin rasboras are great. They stay small and are pretty fast so even if the new betta did get a bit grumpy, they would be too fast for him to catch. You could have about 6-8 in a 10g with the new betta.