We had some discussion in chat yesterday about this setup and Kendra's plans to now upgrade the tank and relocate her 3 comets to someone's pond (next week).... leaving her with one small oranda and a black moor. (The 10 gallon tank previously mentioned will probably be used for guppies.) She also has a 55 gallon tank she can work with in the interim.
For right now while the comets are still there, start doing 20-30% water changes every day and rinse out the small filter you're using every 2 days or so (that you can begin to estimate better by appearance, btw.) Clean the bottom thoroughly using a siphon (python works great if you have one of those).
Regardless of the timing involved getting a new tank setup or moving the fish over to your other tank, the first thing you're going to need is a reliable test kit so you can monitor the parameters closely. This is something you can't put off and you can't skimp on. Get the API freshwater master test kit that Lupin recommended. With that, you'll be able to measure exactly what the levels are for ammonia, nitrite, and nitrate. By doing this, you'll be able to see when you need to do water changes and get an idea exactly how much water needs to be changed each time. With that, start testing the water regularly to keep the ammonia and nitrites at or (very) near ZERO at all times and the nitrate level below 40 ppm. Even a slight trace of ammonia or nitrite is toxic to fish, so this is very important. Nitrates at levels of 40 ppm or higher is also harmful for the same reason.
I don't know what state your 55 gallon tank is in, Kendra.. but you should also read this information about cycling a new tank.
http://www.aquariacentral.com/forums/showthread.php?t=84598
If you're only going to keep 2 goldfish now, the 55 gallon tank you mentioned will work just fine. What money you're able to spend for this right away should probably go toward buying proper filters (new or used) for the tank. If you decide to buy another tank anyway, here are some pointers to follow.
Fancy goldfish need 15 gallons of water each and pond types need 20 gallons each. Goldfish are best kept in a group of 3 or more. So a little simple math here will let you decide how large a tank you'll need for the number of fish you want. For the most part, you can use whichever type or brand of filter you want (or can find inexpensively). To estimate that, multiply the number of gallons of said tank (as in 55 gallons) x 10 (times 10) for water movement through your filter system per hour. I normally prefer to run two filters at the same time on a tank of this size or larger, mainly because something is still working even at a lower level of performance if something happens and one of the filters conks out on you. So, for your 55 gallon tanks, try to set up filtration that pushes approximately 550 gallons of water per hour. If you end up running something a little lower than that, it's going to greatly demand heavier water changes to be performed more than once every week.
This is a lot for you to contemplate all at once, I know, so I'll stop right here for now. I also know you'll need to clear some of your plans with your parents, first. If they raise concerns about anything with you, just let us know. We can help you address any questions they might have or possibly make alternate suggestions if you run into limitations with this that you're not expecting yet.
Whatever else you need to know.. just ask. Good luck with all the changes you're already planning to make. You're doing a terrific job the way you've jumped right in to find all the best information you can get! Let us know what else we can do to help you (and your parents) along the way.