What are your pH and hardness values? What kind of cichlids were you thinking of adding?
It sounds like you like the looks of a group of fishes that are relatively incompatible, both in terms of behaviour and water chemistry. Maybe you could decide which fishes are your favorites and then start from there in finding out what other fishes would make good tankmates for them?
I'm pretty certain that no one will recommend "Africans" (a large and diverse group) for a community tank, but Rams (Mikrogeophagus ramirez), which are a much less aggressive and smaller cichlid, or Kribs (pelvicachromis pulcher), which are somewhat less aggressive, but still territorial, are often mentioned as potential community fish. I've never heard of anyone putting Kribs and neons together, however. Maybe with the rams -- I think they both like soft water with lower to neutral pH.
In another thread, Aulonocara baenschi was mentioned as a milder mannered cichlid. I don't know anything about this fish, but if you do a search on google, I'm sure you'll find something.
Since you have a good sized tank there, you might consider another variety of Krib that is larger -- and also likes those softer, lower pH values. Here is a link:
Giant Krib
Still, I think you've got some research to do before you start buying fish. I myself would not mix livebearers up with cory cats, because I would salt a livebearer tank somewhat and I wouldn't salt a cory's tank, or a cichlid tank either. There will be people who disagree with this. It's just my own opinion. I wouldn't put cory cats in with kribs, either -- I would get a synodontis, like the upside-down catfish instead. Cichlids shouldn't bother the synodontis.
Nor would I have neons in a new tank, particularly if I had anything less than their ideal parameters (i. e., soft water, etc.). If I had my heart set on that type of fish, I would try to find cardinals instead, which are both larger and hardier, and I think prettier, too. But I still don't think I'd put them with cichlids. Maybe a big school in a tank that size would be ok with lots of plants. Maybe not. I have no idea.
I'm sure you'll get a bunch more opinions on this. Take it slow and you'll figure out something that will work for you. Good luck!
Alia