Looks like you have Malawi's. There's three main types of African cichlid based on the rift lakes Lake Malawi, Lake Tanganyika and Lake Victoria. There are also other Africans outside these three lakes but you are unlikely to run across them too often in the hobby on the most part. As a general rule you don't want to combine fish from differing lakes, so being as you have Malawi's you are best to stick with other Malawi. The lakes are vast and there are heaps of differing species, this means there are also specific groups of fish even within each lake. Based on your pics I'd say you are best going with "Mbuna" which is a group of Malawi species that live in the rocky areas of the lake. Mbuna are all fairly aggressive and are dense in population in the lake, for this reason you want to have the tank stocked fairly heavily (moderately overstocked) and it's best to provide decor with many caves, tunnels and hiding spots. The idea is to stock the tank heavily enough so that there's so much activity, running in to different fish etc. that none are specifically singled out to be targets of bullying. The orange fish in your last picture (Red Zebra) I have found is particularly bad for harassing others if you don't have enough tankmates and/or hiding spots.
There's a good range of species you can get within the Mbuna group and they are highly common at most fish stores etc. Actually they probably make up the majority of African cichlid around in the hobby so you wont be bored or too limited with the options. They are highly active and colourful also so a 120gal tank will be impressive and entertaining to keep. People actually say a Mbuna African set-up is as close as you can go to a SW aquarium without actually having a SW aquarium as far as colour is concerned. The behavior between the fish in any large African set-up is awesome as well.
It is difficult to say a specific number of fish in 120gal other then to say quite a lot. As long as you stick within the Mbuna group it would probably be best to buy groups of fish 4 or 6 at a time as you get the tank going and step up that as you go asking about adding another group or not. There are differing preferences amongst some species for ratio male to female etc. but this is too wide to offer you specific advice as there are too many differing species and general factors like what other tankmates (or pairs) you have, the personal availability to you where you are getting the fish and sexing them etc.. I don't think you'd go too wrong though in 120gal if you start with your current fish, add a group 4-6 fish and then go from there as long as you stick to only Mbuna.
You may want to look at running more filtration as cichlids are messy eaters and produce a lot of waste. This depends a bit on your current canister filter but with a Malawi set-up stocked well in my opinion you would want to be turning over 10 times the tanks water volume or more per hour through a decent amount of filter media. Malawi also tolerate (could be argued enjoy) a fair degree of water current so you could run powerheads/internal filtration or Hang on style filters also if you wished to achieve a high turnover and more filtration. It is possible to run lower then what I'm recommending but maintenance will be higher on the tank and because the fish like a fair amount of decor, rocks etc. you can have problems with dead-spots in the tank if you don't have decent water movement and turnover.
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