Once you get the new tank please remember to cycle the filter before adding the fish. You can speed up the cycling process by putting mature media into the filter. I often also pilfer substrate, live plants and other tank ornaments like wood from an established tank and put it into a new tank because the benficial bacteria will be colonised on everything in an established tank. Even doing this you will need to keep a close eye on how the tank is establishing/ cycling and even more so after you add the fish while the bacteria play catch up to the new levels of bioload. Also if you do use mature media remember to feed it, dont just leave it in the tank with no food source, otherwise it will just die and all your efforts will end in vein.
It is an often heard cry "I wish I had researched more before", but at least you are now doing that research and taking on board all the suggestions and trying to now do your best for your fish, this will not only make the hobby of fish keeping more enjoyable to you, but will also give your fish long happy lives, which ultimately all of us are striving for.
Suitable tank mates for corys are anything peaceful and nonterritorial especially around the floor of the tank, similar water temp and pH, gH requirements too will go a long way to the easy keeping of the fish. Almost anything from the Amazon (excluding cichlids) will be good with corys, but you can also get soft water Asian, even Australian fish which are also peaceful.
Also live plants are a huge boon for any tank, not only do they grow and multiply allowing you to spread them out through other tanks or sell the excess, but they are soft and dont injure fish like some plastic plants can. Live plants also help in the whole ammonia/ nitrogen cycle. If you are worried about having to go down the high tech route for plants the simple answer is dont. There are lots of easy grow low care and basic lighting needs plants that will still do all the good for the tank that any high demands plants will do. Just a word from the wise (i.e lesson learnt the hard way) its not a good idea to add java moss to tanks with corys, my corys love snuffling and bumbling through the java moss. Knocking it loose from its timber and rock strong holds, only to be sucked into the filter intake and clog up the filter.
Oh and CONGRATULATIONS on getting 3 more corys