Keeping fish is a great hobby with will keep kids out of trouble at least for a while. But this hobby is not something like Collecting Stamps or those superhero or baseball cards. Here we are talking about live fish which feels hunger as well as pain. Basically its same like having a dog or cat in many ways except you cant hug them. So if you are planing to let your kid to have a fish then make sure you re-plan it and make sure your kid understand what he is get into. Also you need to understand what you are getting into. In most cases you will be the one who taking care of it.
There are several big NOs. These things, you should understand as well as explain to your kid. It's important he/she/they learn how to take care of the pet fish properly.
Don't buy those tiny fish bowls for them. No matter what people say Those glass bowls are a very bad idea for keeping fish. No Fish like to live in tiny space like that. It's a big no for Goldfish and even for Bettafish its not good. Remember natural habitat of Betta fish are big wet lands, swamps and paddy fields which are miles and miles long. They love to swim and explore. Please make sure you understand this and teach this to your kids too. Nobody like to stuck in tiny room.
Don't get those single tail Goldfish like common Goldfish or Comet Goldfish from Carnivals etc unless you plan to have a 4 Feet / 60+ gal fish tank. Goldfish types live long and get very big. Unless you have space / money for this don't let kids to get those fish even from a pet shop.
Don't buy fish that too expensive and not easy to keep. For example Discus Fish are very beautiful but they are very expensive and you need advance level of experience to keep them. They need frequent water changers, special food and have to be very careful about tank makes.
Don't buy fish right away when you got a pet fish. Either pre plan what type of fish you are buying. You can research on net with your kids about it. Let them to learn all about the fish they want to have. Or When you are at pet shop take photos and ask names of the fish they like and research about them. After that you can buy.
Always go for easy to keep, small and hardy types of fish. Good examples are Tetra, Platy, Molly etc. First buy just a couple of pairs and let them to keep these fish for a while. Make sure they don't loose interested before buying more. Let them to feed fish once or twice and day and teach them about right amount of fish food to put.
Don't buy everything same time. First you need to buy the Tank, Lights, gravel and Filters. Setup your tank and let it settle few days before putting fish in.
Buy your kids about the fish they have / going to have or about Fish Keeping. Read the book with them and discuss about it. Make it more interesting for them and also useful. These books can teach them a lot and It might help you to avoid future fish disaster or 2.