First: You don't need to wait 30 days to add fish if you follow what I'm about to tell you.
Second: Goldfish don't have intestinal tracks so what goes in immediately goes out so they are really dirty and shouldn't be kept in a filterless aquarium but if you must keep them in a bowl, do 1. It is NOT true that fish grow to the size of their tanks, their outside body does but their internal organs don't, eventually their organs will get too big for the body and they will die. So it's best to do an inch per gallon. Minimum goldfish should be in a 20 gallon tank but I understand if this is your first time and you want to try things out you will get a bowl. I just want to be clear that if you want to be successful and really love having fish, go bigger with a filter and you won't regret it.
To shortly describe the Nitrogen Cycle to you, the nitrogen cycle happens when you have fish, when you first get a tank it goes through what is called "New Tank Syndrome" during this period of time is when you DON'T want to add fish, the reason being is that beneficial bacteria is needed to start the nitrogen cycle eliminating any toxins such as Ammonia, Nitrites, and Nitrates. Ammonia is the #1 killer of fish so in order for it to be transformed into its lesser toxic state called Nitrate it must have beneficial bacteria in the tank. How do you do this?? Well you can buy beneficial bacteria to start that process.
Say you just started your tank, set it up put all your decor and then water. Instead of putting fish in that day, you can go to your local pet store and pick up beneficial bacteria, I'd suggest API Stress Zyme, you'd also want to pick up Stress Coat which is a water conditioner. For the rest of your fish keeping hobby you'll want to use both whenever doing water changes, whatever bacteria you take out, you must put it back in. So you'll double the dose on your tanks first setup so say you have a 10 gal you'll want to treat it like a 20 gallon. You usually do both Stress Zyme and Stress Coat for the first 3 days THEN bring a sample to your pet store for testing. If all is good then get the fish.
If your fish is at the bottom it means it's stressed out either by being sick, not enough decorations, water conditions, or bullying. Stress Coat is a water conditioner but it also has aloe vera which puts the fishes natural slime coat back on it's body when it stresses out, eliminating any chance of getting sick.
If your fish is at the top gasping for air it means that the ammonia levels are really high. Not to scare you or anything but this is the truth, ammonia burns gills which stops a fish from being able to breathe, which is why you might have seen them at the top or the very bottom.
I would suggest buying a bigger tank, if it can be done get a 20 gal and a Aquaclear filter (Literally the best and will make your life so easy) Get Stress Zyme and Stress Coat, double the doses of both so 2x of 20 ml each or full cap, and let your tank run for 3 days before adding fish.
If that can't be done then still get the Stress Coat and Stress Zyme and if your bowl is 1 gal just double that dose by the instructions on the bottle. Still wait 3 days.
Make sure you keep up on changing your carbon every month if you have filter, you should be doing monthly water changes of 25% or weekly of 10%.
If you decide to get the Aquaclear filter, don't wash the sponge or bacteria blocks in fresh water if they are dirty, instead wash them with the tank water you pulled out during the water change.