It's ok to have a lot of questions, so long as you have time to read a lot of answers.
First of all, the letting the tank sit for a week is fairly inaccurate. Just having water sit isn't going to show any nitrate, or ammonia because there is no source for it. Both of these come from waste. Which isn't in the tank. What you need to do is
cycle your tank.
However, This type of "fishless cycle" cannot be done with fish in the tank. It will surely kill them. So you have two options.
a) Take back the fish you got to the pet store for store credit (tell them they were dumb for selling you fish, knowing that you hadn't cycled the tank) and begin the fishless cycle.
B) Keep the fish in the tank and do what is called a cycle with fish.
Beware this is generally considered to be pretty cruel on the fish and you will probably recieve a fair bit of ridicule. This method involves daily water changes to help reduce the waste toxins building up in your tank.
So, next for how many fish to buy, the very general rule is one inch of fish per us gallon. This however often requires adjusting for large fish (obviously a 20 inch fish won't fit in a 20 gallon tank) High waste producing fish (plecos) Or really active fast swimming schooling fish.
A bucket is fine for water changes. As long as you have never used it to hold anything that may be harmful to your fish. Soap, whatnot. Most aquariusts have invested in a nice fresh bucket for their fish.
Good luck with whatever you choose to do.
Just my 2 cents (try to avoid the cycle with fish, I am one of those who think it's pretty devestating to see the effects of ammonia on the fish.)
