Redtail black sharks and rainbow sharks do best on their own (1 per tank).
I would get 6 angelfish and if you want to breed them, get 8-10 the same size and add them together, then grow them up and let them pr off. You should get a pr from 6 fish.
Corydoras and medium to large cichlids don't always work well. What is the parrot cichlid like, does she bulldoze everything and move stuff around, show aggression to the other fish, or is she mild mannered and just does her own thing?
If she's mild mannered, then Corydoras might work. If you get Cories, they do best in groups of at least 6 (preferably 10) or more.
Most deep body tetras do better with rainbows than small narrow fish. Things like black phantom tetras, red phantom tetras, diamond tetras, rosy tetras are all higher in the body than neon tetras and much less likely to be eaten. However, most tetras and angelfish come from soft acid water.
Barbs are an option and like harder water with a more neutral pH. Black ruby barbs, rosy barbs, golden barbs, are nice and get along with rainbows and usually do alright with medium sized peaceful cichlids. Rosy barbs might be a bit boisterous or active for angelfish. However, if the angelfish are fine with rainbowfish, they should be ok with peaceful barbs.
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What is the
GH (general hardness),
KH (carbonate hardness) and pH of your water supply?
This information can usually be obtained from your water supply company's website or by telephoning them. If they can't help you, take a glass full of tap water to the local pet shop and get them to test it for you. Write the results down (in numbers) when they do the tests. And ask them what the results are in (eg:
ppm, dGH, or something else).
Depending on what the
GH of your water is, will determine what fish you should keep.
Angelfish, discus, most tetras, most barbs, Bettas, gouramis, rasbora, Corydoras and small species of suckermouth catfish all occur in soft water (
GH below 150ppm) and a pH below 7.0.
Livebearers (guppies, platies, swordtails, mollies), rainbowfish and goldfish occur in medium hard water with a
GH around 200-250ppm and a pH above 7.0.
If you have very hard water (
GH above 300ppm) then look at African Rift Lake cichlids, or use distilled or reverse osmosis water to reduce the
GH and keep fishes from softer water.