The most popular species of freshwater aquarium fish are goldfish. The reason why goldfish are so popular is because they can stand almost any condition. That doen's mean I'm suggested you buy a small bowl and put your goldfish in there. In fact, I suggest the opposite and advise you buy a large home for your fish together with filters, pump, plants and water cleaning products.

There are ov er 100 different species of goldfish. The most popular ones are:

Comets, which have a long tail and skinny body.
Fantails, that are shaped kind of like a fat egg. They have double bottom and tail fins
Veiltails have log flowing fins, and are very popular. Some of them have telescope eyes that stick out on each side of their head.
Shubunkins have a big tail fin, and come in many colors. They are very popular for ponds.
Black Moors are all black, have telescope eyes, and veiltails.
Lionheads have a bumpy growth on their head that kind of looks like a lion's mane. They don't have a dorsal (top) fin, and a double caudal fin.
Bubble-eyes are one of the oddest goldfish. They have large sacs below the eye that look like someone blew their bubblegum and stuck it under their eyes. Like Lionheads, they don't have a dorsal fin and can't swim too well.