Ya know...fishtanks are really fun and one of the reasons that I got into them in the first place was because of exactly like you said, I liked looking at them in other people's houses and I love going to the aquarium
Best thing you can do is keep an eye out for a good size tank at garage sales...its starting to be summer and buying a new tank just doesn't make any sense. If you were to try to put more fish in the tank than will fit (we call this overstocking) or dont do regular maintenance or don't do your homework on what fish will work together...then it could end badly...however...the flipside is very reasonable. If you don't overstock, you do your homework on which fish will work together and work in your tank and you do some simple regular maintenance a fishtank is pretty easy to take care of and enjoy! I am pretty bad about doing maintenance myself, so one thing I make a point of doing is under stocking my tanks so that if I go further between water changes it isn't the end of the world.
If I were to do everything all over again here's what I'd do:
1: Buy a 29+ gallon tank with a stand and a hood at a garage sale or off of craigslist. I wouldn't pay more than about 50 bucks unless it is a really large tank. Most people start with a small tank thinking a small tank is easier and then they get discouraged when things don't go right and they get out of the hobby...if only they knew that a larger tank is easier to get going because it is more forgiving. Once you get your tank home find a good spot for it where it is visible, relatively close to a faucet and won't be getting direct sunlight. Either outside or in a bathtub/shower you should also test that your tank holds water. Don't fill it up really quickly or with really hot or really cold water...fill it up slowly and run your hands along all of the silicon seams as tanks that have been dry for a long time can be brittle. If you pop a seam you will be very glad that you did so in a bathtub or outside rather than your living room. Once it's filled up...dry the outside and strategically place some paper towels and walk away let it sit for a couple of hours and make sure there aren't any small leaks.
2: Go to an online retailer like bigalsonline.com or local store and purchase the following: a python (not the snake...a python is a hose that you use to make water changes easy!) and a faucet connector and a gravel siphon that fit onto the python, freshwater test kits for Ammonia, Nitrite and nitrate (all of which should come in a kit if you want to get that like the aquarium pharmaceuticals master kit or whatever they call it), get either an eheim canister filter or an aquaclear power filter that is rated for a tank your size (or a bit larger if there is a question), and a bottle of prime (water conditioner (dechlorinator).
3: Even before you get your tank, you can start doing some research online (like reading the FAQ's and posts using the search feature here on MFT) as well as window shopping at your local stores. DONT BUY ANY FISH and be polite, but take anything a pet store employee tells you about fish or fishkeeping with a grain of salt because a lot of times they have no idea what they're talking about. (You hear a lot of us mention this because at one point or another we have all seen it and most of us have had to learn the hard way
) Looking at your local stores will familiarize you with some of the fish that are locally available...so you can go home and read about a fish you saw to see if it is easy to keep etc.
4: Once you think you are ready to put water in your tank you have to decide if you want to do fish in or fishless cycling. This is the most frustrating part of setting up your first tank...and its something that will happen whether you pay attention to it or not. The "cycling" process we refer to is what happens when someone is first setting up a tank, before the tank gets "established" and able to handle fish...it goes through a period that is dangerous for the fish. Thats why when you hear about people who get really frustrated with their fishtank when first setting it up because they cant' seem to get fish alive...its probably because they aren't watching the water chemistry and don't know that they either need to do a LOT of water changes for the first few months or be adding in something like bio spira or be doing a fishless cycle.
THEN you can go about getting some fish...and if you've done your homework and are prepared to cycle or have your tank cycled...you should have a lot of time to enjoy your tank.