Hi Mily,
You're very smart to ask the questions before you run out and get a tank and fish. I would suggest visiting pet stores and also reading a couple of books. If you see a fish you like, read up on it and see if it's a good community tank fish or not. You don't want your new fishies attacking one another. Also, some fish eat or uproot plants and if you like the look of live plants, that can be aggravating or expensive.
Good book: Innes's
Exotic Aquarium Fishes: A Work of General Reference (used copies available on Amazon for 10 cents!)
Decide how big a tank you want and can afford. Some fish need more room or more current in their water than others. You want to provide a suitable home for your new pets or they will get sick and possibly die. At the very least, they will be unhappy and unhappy fish don't look their best.
The worst this most new hobbyists do is to overcrowd their tanks. The rule of thumb for tropical (freshawater fish is one inch of fish (length) for one gallon of water. So if you buy a ten gallon tank, you can support one big fish or a small school of neon tetras. Just don't overcrowd them.
Talk to people at your local pet store about different filtration systems. I know some people who spend a ton of money on these but sometimes a plain old-fashioned box filter in the corner will do the trick. You may decide you want one of those filters that hangs off the back of the tank. Or you might go all out and buy a protein skimmer and all the bells and whistles. The filter will keep the water clean for the most part, but you will need to do periodic water changes. Innes has great information on this process and how much to change at one time - everyone has their preferences and talking to other hobbyists is a good way to learn alternatives. Some of it will depend on how much you have to spend, how dirty the fish in your tank are, whether or not you have live plants (rooted plants don't do well with undergravel filters), and other factors.
Regarding water changes, check with your local water district and find out when they add chlorine and anything else to the water supply and don't change your water right after that - give the chemicals a few days to dissipate.
One of the other forum posts has a list of fish hobbyist clubs. If one is close to you, please go to a meeting. Not only will you find people who love fish as much as you do, they can answer your questions and offer advice. Fish keepers love to help each other out and you might even find out about varieties/species of fish that aren't in the stores.
Let me know if you have more question and bravo for wanting to move to a bigger tank. I think you'll enjoy it a great deal!