Shekes is right about the liquid bactria you can buy and you don't NEED tet kits for freshwater tanks, but they are nice to have. I am assuming you started with new filter media and added all the fish at once, if so what happened is the fish waste produced ammonia faster than the new filters bacterial colony could keep up. Here is a simple way to start a new tank from scratch.
Set up your tank where you want it making sure it is level and fully supported evenly.
Add your gravel/sand after it has been thorughly rinsed, then fill the tank with dechlorinated water, Add the filter and heater and turn them on, take a couple days to make sure the temp. stabalizes where you want it, for most tropicals that is around 78-82 degrees F.
Add plants if you are going to, then wait another 2 days, this lets a bacterial colony get started in your filter and lets you check for hitchhikers like snails and hydra.
Add 2-3 fish, preferably the less territorial or less aggressive ones, then wait 2-3 more days, don't over feed, they will produce some waste but the bacterial culture in the filter will catch up quickly.
Add a couple-3 more fish and wait a couple more days, repeat this adding of fish and waiting until you have reached the stocking level you want. This lets the bacterial colony grow to keep up with the level of waste being produced.
Don't over feed and remember to do partial water changes regularly, 30% every week is good for most tanks, less often if the tank is lightly stocked, bigger changes if the fish are messy eaters or you have a heavily stocked tank.
The only thing I can think of that would cause a tank to break like that is if the support was incomplete or uneven letting a part of the tank settle and stressing the glass.
Goo luck and welcome to MFK.