Came back because people were asking questions about set-ups and I had some thoughts.
1: If you're starting out new, don't do the seemingly rational thing of getting a small or nano tank. Five gallon tanks are nice and compact, but they can be a nightmare to maintain, especially if you're going the route of natural substrate and living plants. Things like hair algae and invasive snails can piggyback from the fish store to your tank and wreak havoc on your water parameters. Also, nano tanks are only good (read: adequate) for a very limited list of fish. Bettas and guppies are fine, and so are tiny schools of things like endlers and dwarf tetras/rasboras, but anything else will not be happy in such a tiny space. Overstocking a tank this size can kill your entire stock in a real hurry. Keep in mind that all-in-one set-ups have less available water space than advertised- a 5g tall tank only has 4 gallons of actual swimming space.
2: Ten, fifteen, or twenty gallons is a good start. It takes up more space but there's a glut of appropriately sized heaters and filters on the market. The filter is the most important part of keeping your fish alive, so don't skimp out. Rim-top filters (the ones that have the waterfall outlet) are adequate enough for a tank of that size, and will introduce enough aeration and flow into the tank that you don't have to worry about buying airstones and shit like that. Again, there are limits to what kind of fish you can put in a tank that size- no cichlids, no oscars, and only a limited number of corydoras/catfish. I don't know much about the keeping of cold-water fish but I'm pretty sure twenty gallons is considered the absolute minimum for goldfish.
3: Goldfish are absolutely not tropical fish, and are best kept in minimalistic tanks with no plants. They'll tear up anything else and got a bad habit of ripping their fins on rocks or any sharp decorations you put in their tank. They cannot be in a heated community tank with other fish.
4: (And this is the number 1 barrier to people jumping into fish keeping), you got to be patient with a new tank. Filling it up with rocks and water then dropping fish in will almost always end with those fish dying from ammonia/nitrite poisoning. If possible, you want to introduce enough living shit into the tank to kick start the nitrogen cycle and have it go quickly. If you've got a friend that keeps fish, ask for some of their tank substrate, or plants, or pieces of driftwood that have already been sitting in an aquarium for a while. Take the gunky sponges from another tank's filter and, after a quick rinse, drop them into the new tank. Those things are teeming with critters that will populate your tank and filter and make it so that all the toxic nitrates/nitrites produced by your fish are processed. An explanation of the cycle and tank processing is
here.
5: Read about every fish you want to buy, before you buy it. Every chain petstore you go into provides extremely limited information about the fish they're trying to sell you, and they do that for a reason. Oscars are cute and small as babies, but they are capable of growing up to 11'' in their first year and will end up eating all those other cute baby fish you bought to be his friends. The siamese algae eater you buy to control algae in your tank is going to grow from a half inch to five or six inches, and need a whole lot more swimming space than a ten gallon can provide. The chump trying to sell you a pleco 'to clean the tank' isn't telling you that plecos don't eat fish poop and that some plecos can grow to be a foot and a half long. A lot of fish will only thrive if they're purchased as a group or school. Every fish has their species profile, and you should give a shit about putting them up in a tank that can give them what they need in terms of space and swimming habits.