Miskairal is really right about the surprises we encounter these days in setting up aquaria. Cycling a tank has always been important, but only talked about in the last couple of decades. It did seem so much easier "back when."

First, a couple of questions for you. Do you want a conventional community tank? Or would you want a slightly different livebearer community tank where a few especially hardy and clever fry survive to grow up?

Those above, kind of go with, "What is your pet store's return policy? Will they take fish back, oh, in trade for ammonia, nitrate and nitrite testing kits? " ;)

If you wanted a straight community tank, keep your two Corys and maybe four other fish for now. Be aware that sometimes, even with freshwater aquariums, it is best to add the least assertive fishes first and more aggressive (or larger) ones later.

If you want fry, keep the Corys or the spotted pleco and maybe four of the livebearers. Along with the testing kit, get some floating hornwort and a few Valisnaria plants to plant along the sides and back of the tank.

I don't know what to say about that "spotted plecostomus". There are over 1,000 of the suckermouth catfishes and at least scores which have spots. Some stay small, a couple (the clown pleco of the genus Peckoltia) stay small but also get territorial and it is wise to have only one in a 30. Some are food items in the Amazon basin. They will usually thrive on spirulina wafers, veggie tabs and/or several green veggies (sliced zucchini, sliced cucumber, peas, maybe Romaine lettuce, but not most lettuce.)

When time permits later on, visit http://www.planetcatfish.com/core/index.php or Google spotted pleco.

Your concern about the water changes are most appropriate. The three 20% ones a week are enough, though we don't know for sure what the ammonia is doing with that population. You do need to let some in ammonia stay in there to get the cycle going.

Also, if you get a chance to season your changing water for a few days, it will lose a lot of its chlorine (unless you have chloramines = chlorine + ammonia) and a little free nitrogen. And it will have a chance to absorb some free oxygen. There are different water conditioners appropriate for different waters. See http://www.guppylog.com/story/2003/10/29/1074/5757

We just discussed the fishless cycling here, where one buys and adds a certain amount of ammonia and uses the test kits to the monitor the ammonia spike, the decline of the ammonia and a nitrite spike and then the settling down of those first two figures and the rise of the nitrates – which is a good time for a water change.

See http://www.guppylog.com/story/2004/9/22/20843/5101 for a good discussion of the nitrogen cycle.
http://faq.thekrib.com/begin-cycling.html
http://www.guppylog.com/?op=displaystory;sid=2005/6/30/161112/322 gives some URLs of interest.
http://badmanstropicalfish.com/articles/article14.html described fish-less cycling, maybe for lurkers.
http://www.thetropicaltank.co.uk/flc-data.htm a sample case.

It is a good idea to treat new water but not the tank with Prime. I believe, as with Amquel and a bunch of other water conditioners designed to deal with ammonia, it bonds it chemically and the ammonia is slowly released into the system, so there is not an ammonia surge, But as you have noted, that also impacts and can set back the cycling.

Related to that, do you know if your water supply has chlorine or chlorine + ammonia = chloramine? Small towns are (at the moment) more likely to have just chlorine, but major metropolitan areas (and the small towns they supply) are more likely to have both. One usually can call one's village water department. They or someone in the office - should be able to answer that straight off. They should also have a report to the EPA, which, when you have time, you might arrange to pick up. Stuff one couldn't care less about, suddenly takes on meaning when we either get fish or a baby in the family. ;)

That Bio-Spira, to jump start the cycle, is a very interesting idea. (I cheat and take a lot of water, gravel, plants and even filters from established tanks. If you were around the corner in Chicago's Southern Suburbs, I'd be lugging water, "used" gravel, Najas and maybe a filter over - not for the first time.) Peter suggests, in that 3rd URL above, that the stuff needs to be refrigerated. I have no experience with it. Check with the pet supply manager.

If the shop will not take some of the fish back -  or if you don't want to take any back - hang in there until that Bio-Spira comes in. Feed sparingly and the fish will produce less waste. It is hard in this weather, but if you can keep the tank at 75-76, rather than higher, their metabolism rates (and aggression and maybe courting behavior) will moderate a little.

It may be possible to cycle that 30-gallon tank with that crowd in there. Be moderate in feeding. Watch for the Bio-Spira. Your observations on the various fish ring pretty true. If the test kits are affordable (with trade ins or as a regular purchase) I think that they would actually serve to relieve you of a lot of uncertainly and anxiety.

Your pH sounds fine. Municipal water supplies are supposed to be more or less in that range and that is great for livebearers. PH was one of the first things aquarists and field workers began testing for many years ago. While disasters can accompany really high or low pH reading, there are a whole lot of other tests and readings which I believe are of greater important to you now and later in the hobby. It has been 25 years since I bothered to test for pH. Still have the kit which is probably useless anymore.

Your evaluation of your fish rings pretty true. It would be nice if "they" would at least take back the lonely  glass catfish, the female molly and the over-sexed male neon sword. ;)   Bettas may or may not be a good match for that crowd.

The bit of salt Miskairal is suggesting, maybe a tablespoon (not of table salt though) for your 30-gallon tank, is an old pet shop trick. It enables their fish to endure more nitrates (and maybe whatever) in over-crowded tanks, at least for a time. Good idea! (And thank you M. for untangling the sequence - again.)

That tank, when cycled, is a great match for a few swordtails though. There will be some bumps in the road, but it sounds like you are making some considerable strides in catching up with what you need to know and do. Hopefully something here will be of additional use. Please keep us posted. :)