The basics for freshwater fish: tank, gravel, some plants, a filter, food, thermometer, a small net, stress coat or similar product or filtered water. You could also use a small test kit, which is useful especially in the beginning when you're cycling your tank and trying to make the level stable. However, I know petsmart tests your water for free, so that's another alternative. You might need a heater depending on the temperature in your house and the kind of fish you want. Certain kinds of fish are more sturdy and can handle changes in temperature with relative ease, but others find it highly disruptive.

now, as for the basics for a saltwater tank: a lot of money.