A brand new tank, being stocked with its first inhabitants? I might be persuaded to bypass quarantine; otherwise, quarantine is a must, IMHO. Adding new fish to an established tank without quarantine is like unprotected sex; you might be okay...but you might not...and if you continue to do it you will eventually lose the coin toss. The cost of the fish is a non-issue; if you have a tank full of inexpensive fish which you have maintained and grown up for months or years...and you then lose them to an unknown pathogen introduced with unquarantined new fish...are you really going to say "Oh, well, they were cheap!" Once you invested time and effort into your fish, there is more than money involved...never mind the ethical considerations.
How do you set up a quarantine tank? You use a filter to keep the water clean, a heater to maintain the correct temperature, some decor to provide the fish some sense of security, and you monitor your water conditions/parameter to determine if/when the tank is cycled. In other words...you set up a quarantine tank just like any other tank. Once you have established tanks you can keep extra sponge filters in them, which can then be placed into a new quarantine tank to create an "instantly-cycled" tank when needed.
I don't have any experience with bottled bacteria so can't say how well they work, but once your tank is cycled, each time you add fish you are adding to the bioload and thus demanding the bacteria to reproduce and grow their numbers to deal with the additional waste. If I add ten fish to an established cycled aquarium that already contains 50 other fish roughly that size, I have increased the bioload by 20%; the bacterial population will grow quickly and "catch up" to the new, higher bioload within probably a day or two, no harm done. But if I add ten fish to a tank that only contains one fish up to that point, then I have increased the bioload 1000%; the bacteria will take longer to reproduce to the required level, and there will be spikes in ammonia and likely nitrite for several days. This is the main reason for not adding large quantities of fish at the same time.
This should go without saying, but I'll say it anyways: you should have a liquid test kit like the API, and use it to monitor your water parameters to determine when/if you are fully cycled, and how your tank reacts after an addition of livestock.
Finally, try to bear in mind that not all fish are ideally suited to identical conditions. You want Neons, Zebras and Platies, all of which would be happy in the low 70F range...you don't specify which species of Corydoras you like, so that's an unknown...but you also want a Dwarf or Honey Gourami which, in my experience, is much more suited to 80F than to 70F. Compromise at 75F? That will likely work, but...some of the fish will be closer to their maximum, while others will be at their minimum...which means that literally none of them are in their ideal zone. Personally, I would get Cardinals instead of Neons...at least as nice, and better suited to higher temps. Skip the Zebras, and do a bit of reading to see which species of Corydoras will be best suited to the upper 70's...there are many...and then keep your tank around 78-80F.
Or...get the Zebras and Neons and Platies, pick a cooler-water Corydoras like perhaps paleatus, skip the Gourami and set your thermostat to 72F. The point is simply to decide what you like best, and then cater to those species rather than forcing fish together who don't really belong together.
