So, how many cories and tetras can I put in and keep them happy??
At 20 gallons, I would say do no more than 15 inches of fish, just to make sure everyone has enough room. 9 tetras and 6 corys should do it.
Not cycled, no. Didn't know about that. Thanks for sharing! I will do this though. How should I begin with the fish then?
YES!!! This is very important. Before you add any fish, you need to cycle the tank. Cycling the tank could take 4-6 weeks. That's how long it takes for a bacteria colony to build up to deal with ammonia produced by fish waste and uneaten decaying food. If you do not cycle the tank before adding fish, you will have to change the water every day for 2 months, because you won't have a bacteria colony to deal with the ammonia for you.
If you don't have 4-6 weeks to wait, you might be able to use the filter media from an already established tank. If you have a friend that runs a fish tank, they can help you with this. The pet stores won't help you with this. Using pre-established media won't help you bypass the cycle, but it will help the tank cycle much faster. 1-2 weeks usually.
One of the best things you can do for the health and wellbeing of your fish pets is become nerdy-knowledgable about tank cycling.