I like the fact you want bigger shoals of neons and harlies. While 6 is the absolute minimum, the more there are the more naturally they behave. But leave the neons a while. They have a tendancy to just die for no apparent reason in tanks that have been running less than 6 months.
Panda cories - they would be better with a couple more. Pandas are one of the more delicate cories, so it would be worth leaving these till the tank has been running a while after the filter has cycled.
Livebearers (guppies and platies) - don't forget you'll need a 2:1 female:male ratio of platies as well. With 10 female guppies and 6ish female platies, there will be a
lot of fry. These fish alone will overpopulate your tank in no time flat. Even if you intend getting only male platies, they will harrass the female guppies with no females of their own species. And if you got these mail order, I would check with the company that they will sell males and females in the numbers of your choice - and that they can tell the diffference. You'd be surprised how many workers in real shops can't.
If it was me, I would reconsider having so many livebearers. Maybe just one species rather than two. I'd go with platies simply because of how weak guppies can be these days. The trouble is that guppies are just so pretty

I would also think seriously about getting guppies/platies by mail order. There are so many varieties that you would be more satified chosing the individual fish yourself rather than rely on what the company sends you.
So for my tastes and practical considerations (ie fry) I would get either guppies or platies, 6 females 3 males. Given that a mature guppy can have 30 fry every month and platies even more...........
And that would leave you room for 10 of something else. Or a centrepiece fish.
If you were to use mail order, it would be OK to get the harlies, livebearers and if you go that route, the shoal of something else/centrepiece fish. Wait till the tank has been running a few months before getting the neons and panda cories as they do better in mature tanks.
DefinitionsA cycled tank is one that has grown its two colonies of bacteria to deal with the ammonia produced by the fish.
A mature tank is one that has grown these bacteria plus the biofilm together with all the other micro-organisms that live in an aquarium which help to stabilise the water parameters, usually defined as a tank that has been running for 6 months after the filter has cycled.