Hi and welcome to the forum
If you want a breeding pair of cichlids like Oscars or Jack Dempseys, buy 8-10 young fish and grow them up together. When they mature, they will pr off naturally and you either move the prs to their own tanks, or move everyone else out. Most times letting the fish find their own mates will provide you with a good pr, but not always. Sometimes they don't work together and they need to be given different partners. This is where moving the prs into their own tanks come in. If they don't work out, you can swap them around.
Adding 2 or 3 fish and growing them up together might give you a pair, or you might get 2 or 3 males, or 2 or 3 females. And they might not like each other and you could end up with 1 fish.
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If you don't want a breeding pair and only want some colour and movement, then buy 1 of each species, preferably females because they are less aggressive, (get them all the same size), add them to the tank at the same time, and let them grow up together. They will establish a pecking order and have their own territories and normally be fine. However, if you add another fish afterwards, or move the ornaments around, you can upset the balance and then one fish might go nuts and kill everything else in the tank.
Cichlids like Oscars and Jack Dempseys are highly territorial ambush predators. They have their area and wait for something to swim past, then lunge out and grab it. Putting them in a tank together can work sometimes but there is no guarantee.
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Oscars and Jack Dempsey cichlids can easily reach 10-12 inches long and do get bigger.
The minimum size tank for one adult Oscar cichlid is 4 foot long x 2 foot wide x 18 inches high. If you get a breeding pr and have nothing else in the tank, then a 4x2x2ft tank might be big enough, but a 6x2x2ft tank would be better.
Jack Demspey cichlids need a similar amount of space except they are much more aggressive than Oscars.
Years ago in the shop we had a display tank with Central/ South American cichlids. The tank was 8 foot long x 2ft wide x 30 inches high. It had a number of decent sized cichlids in, including a pr of Jack Dempseys. Everyone was happy and fine for months and they all got along beautifully, until the Jack Dempseys decided to breed. We went in one morning and there was a 8 inch black belt cichlid that had been smashed and was barely alive. We moved it out and the next day there was a parrot cichlid that had been smashed. We checked the tank and couldn't see any eggs and the only thing we noticed was the 2 Jack Dempseys acting very social to each other. There was no lip locking or anything, just 2 fish hanging together. The next day they had eggs and half the fish in the tank were dead and the rest were hiding in the far corner. The fish in this tank weren't small wimpy fish, there was a managuense, dovii and a number of other fish and they were all very similar in size, but the Jacks went nuts and took over the entire tank. They even attacked us and the nets we were using to try and get the injured fish out of the tank.
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If you want other fish in the tank, then add them at the same time you add the cichlids, or add the other fish first and add the cichlids a month or two later. But make sure the cichlids are smaller than the other fish already in the tank so they aren't too stressed about being in with predators.
Silver dollars need to be kept in large groups (preferably 10 or more) and most can grow to 4-5 inches in diameter.
Having more fish in the tank can reduce aggression or make it worse, but it also causes the water to go off faster. You need to have a tank that is big enough (long and wide) to hold all the adult fish and make sure they all have their own space.
I'm not sure what the dimensions are for a 125 gallon tank but it might not be big enough for all the fish you want.
Most of these fish will live for 10 years, maybe more, and there are very few places that take unwanted fish that are big or aggressive.
Do you plan on moving in the next 10 years?
Big tanks are a pain to move, and big fish often stress and sulk when their tank has moved.
Are you willing to look after the tank and fish for at least the next 10 years?
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Regarding cichlid care, they suffer from dirty conditions and can develop hole in the head disease, which is caused by a protozoan called Hexamita. Predatory fishes create more waste and higher protein levels in the water and make the problem worse. The easiest way to prevent this disease (or most diseases) is with regular tank maintenance.
You should wipe the inside of the glass down each week. This helps remove biofilm that is home to harmful microscopic organisms.
You need to do a big (75%) water change and gravel clean the substrate every week. And if the nitrates go up above 20ppm during the week, you need to do a big water change several times a week. You want to keep nitrates as close to 0ppm as possible and under 20ppm at all times. The big water changes and gravel cleaning removes fish food and waste, as well as dilutes the number of disease organisms in the water.
Make sure any new water is free of chlorine/ chloramine before it's added to the tank.
When the filter is established (more than 6 weeks old), you want to clean the filter at least once a month. Filter media/ materials (sponges, etc) get squeezed out in a bucket of tank water and the media is re-used. The bucket of dirty water is poured on the lawn outside. A clean filter will reduce the number of disease organisms in the filter and water. Since all the water goes through the filter, keeping it clean helps keep the tank cleaner.
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Throwing this out there. There are smaller cichlids that are much more peaceful and don't grow as big, but they still have plenty of personality. Severums, festivums, blue acaras, Geophagus braziliensis, parrot cichlids, firemouth, etc. Some of these can get along with an Oscar but not with Jack Dempseys.
) so I've had some really interesting experiences with them. Any other questions, just ask. 
