You will want to invest in a liquid dropper test kit. API makes a nice freshwater master test kit that has everything you need to get started. You can buy plain ammonia from ACE hardware (in the cleaning supplies section) to have an ammonia source for fishless cycling. (This part will not apply to you "crucial" since you already have fish in the tank.)
Goldfish:
They can be heartbreaking, and are a lot of work, so if you want something easier, go with the African cichlids as previously suggested. Either way, you will need a test kit. Don't waste your money with the test strips, they are inaccurate and cost more per individual test. You will be testing every day, and sometimes multiple times a day, so just invest the money for a liquid dropper test kit. If you don't mind ordering online, you can find one for $25 plus shipping. Also, I recommend using Prime as a dechlorinator. This will not only save money in the long run, but also help you should something happen to your beneficial bacteria while you have fish. This is not an excuse to try to cycle your tank with fish in it.
In case you are wondering exactly what "cycling your tank" means, here is a brief description (EDIT:: and by brief, I mean long-ish.)
When fish eat, they also poop (simple enough right?) Well, that poop eventually turns into a waste product called ammonia. Ammonia is very toxic to fish and causes the fish to be burned form the chemicals. So, if you have ammonia in your water, what do you do to save your fish from burns?
The first step of the cycling process is colonizing your filter with a type of bacteria that transform ammonia into nitrIte. NitrIte is also very toxic to fish. It competes in the gills for oxygen, and causes the fish to have blood poisoning (aka brown blood disease) and causes the fish to stress and/or die. Now, you have this problem of nitrItes in your water...what do you do?
The second step in the cycling process is colonizing your filter with another type of bacteria that uses the nitrItes and converts them into a less toxic form, called nitrAtes. NitrAtes will not do as much damage to your fish as the other two forms (ammonia and nitrIte) but as the levels increase, prolonged exposure to higher levels of nitrAtes can cause organ failure, stress, succumbing to illness or infection and ultimately death. So...you have these nitrAtes building up in your tank, what do you do to get rid of them, and at what level should you be concerned?
Once nitrAtes reach a level of about 20, I do a 50% water change. The absolute highest you want your nitrAtes to ever reach to avoid any possible side-effects is 40. You will want to continue to test your water periodically for ammonia, nitrIte and nitrAtes to make sure everything is working well.
You will know your tank has fully cycled and is ready for fish, when your test readings read 0-ammonia, 0-nitrIte and the appropriate number of nitrAtes. After fishless cycling, it is common for nitrAtes to be very high, and you will likely need to do quite a few water changes before the tank is ready for the fish.
Once your tank is cycled, and you have lowered the nitrAtes to the lower level, you can start by adding a small fish or two to see how things go. Give it a couple of weeks, then you can slowly increase your stocking level. (This also depends on what "stock-load" you used when preparing your tank in the amount of ammonia you use to cycle your tank, but I am too tired to get all into that, I believe there is a great article/post here on MFK, if you just search for it.)
It is highly recommended to have a quarantine tank set up for any additional fish you may want to add to your tank. Some people don't do this, and I on occasion haven't...the one time I cut it short, my fish got infected, so that risk is up for you to decide.
I know it may seem a bit overwhelming, but it is also very rewarding when you do it right, and don't lose any fish because you didn't make them suffer through the cycling process/high levels of toxins in the water. It will also save you a lot of money in the long run.