Appropriate fish for my tank?

Question
I just received a 5 gallon aquarium from my girlfriend and am in the process of setting it up. Thus far, I added the interior decoration and water, but no fish yet. The water has been in the tank a week now with the filter running and I also added the de-chloronizer and a a bio agent that was recommended by the fish store to start producing beneficial bacteria.
Now my question is about what kind of fish and how many fish I should add to the tank? The tank also does not have a heater, so I am thinking about adding something that is hardy and less temperature sensitive. I like cory cats, but I hear that preferably they should be kept in a school, is this true. I also like mollies, tetras and many other types. I also like goldfish, however I hear that they cannot be kept with other fish, is this true and are there any fish that goldfish can be kept with? To be perfectly honest I really do like catfish a lot, but I am concerned about whether they are suitable for a community tank, as well as about temperature requirements? I also Love Betas(Siamese Fighting Fish), but once again I don't know how compatible they are with other fish, especially if I am considering adding guppies,  since I hear they go after their tails?

Anyhow, I would like to have a variety of good looking and hardy fish in my tank...so any advice will be greatly appreciated... and Thank You in Advance!!!

Sincerely, Kris

Answer
Dear Kris,
It would be better if you could buy a heater if you are going to keep a betta or any of the other fish you mentioned.  It would be more difficult to try to keep a goldfish in a 5 gallon tank due to the amount of waste they produce and the tank would get dirty  faster since it is only a 5 gallon.  You could try a betta with a small school of Harlequin Rasboras or even some small Tetras. A Dwarf Gourami could also be kept with the Rasboras or Tetras but I wouldn't try keeping a Gourami with a Betta. Cherry Barbs would also make a nice addition.  You could also put Guppies but they will reproduce very quickly and you might be overpopulated very quickly. It would be better to just put males or females to avoid this.  The Cory Cats do like to be in schools and it might get too crowded with a school of them. Just be sure whatever fish you decide on that you don't overstock you tank and don't add too many too fast so you tank won't have an ammonia spike.  That could kill you fish.  Add fish slowly to avoid this and wait about a week between adding more fish.  Be sure to  do frequent water changes at least 2 times a week and test your water just to be sure the water is in the safe parameters for your fish. It would also be a good idea to buy a water conditioner that removes or neutralizes ammonia, nitrite, and nitrates. A water test kit would also help determine your water conditions and this helps your fish to remain healthy.
Best of luck with your new aquarium!
Hope this helps,
Karen