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
I do not ever suggest goldfish because I find them dirty, and I never suggest guppies because I think they have a high death rate.  This is from personal experience and are just my thoughts, others will probably tell you the opposite.
I have a five gallon along with many other tanks.  When it was full this is what I had. (We call this our geriatric tank since all the fish are elderly, so some of them have died.)
I had 4 neons, 1 male betta, 1 red eye tetra, and a snail.  They lived very hapily for a couple years, 2 neons and the red eye are still going strong in the tank.

You can have a male betta with other NICE community fish, NO FIN NIPPERS.

I think 5 gallons is too small for catfish, so I would not suggest them at all to you.

Another thing to be careful of is tiger barbs, many people end up with these because they are small and cute, they don't know they are the meanest little fish, so unless you are going to have them alone, don't get these guys.

Good luck!