It's wonderful to hear you have taken your little goldfish's care to heart.
Goldfish are one of the "dirtyist" types of fish you can get, meaning they create a lot of waste that turns to harmful ammonia in the water. They can also get large, if they are well taken care of and live long enough, so your idea for a 30g tank is a good one.
You *should* get a filter for them, and one that removes waste as well as keeps the biological filter healthy to transform all that ammonia into nitrate. It will cost a little money but the *great* news is that you will only have to change 10-15% of the water every couple weeks, and the fish will be much happier.
While there are small, cheap filters available, they will not do much good for three goldfish and you'll be wasting your money and become frustrated. You will thank yourself in the long run if instead you get a cannister filter that will sit below the tank, under the stand. It sucks water down into the cannister by gravity feed, then pumps it back up into the tank through a spray bar that disturbs the water's surface, adding oxygen. The cannister is filled with several types of media to not only strain the water of impurities, but grow good biological bacteria. I think wiseGEEK has an article on cannsiter filters.
Cannisters are by far the best and most efficient filters for removing waste (needed for goldfish) and keeping a healthy biological filter going. They are also the least trouble, as they only need occasional cleaning (maybe every few months to once yearly depending on the size of the cannister vs your fish load), and they are the only filters worth every penny they cost, imo, after 20 years of fishkeeping.
A large hang-on-tank filter would be next in line, but will require weekly or bi-weekly cleaning and won't do the job of a cannister. They cost about half of what a cannister costs. ($50 vs $100.) I know it sounds like a lot of money, but it's just one outlay that lasts years, and totally worth it for all the pleasure a tank and fish can bring to a house... not to mention the trouble/time it saves you.
And yes, you would cycle the 30g first, fishless with the filter installed, then add the fish once the tank is cycled.
Another good addition, if your pocketbook could handle it, would be an undergravel filter. These are inexpensive. They consist of a plastic filter plate under the gravel, with a plastic feeder tube on one or both sides, rising to a small motor pump (called a power filter) that sucks water up the tube, drawing tank water down through the gravel. This keeps the biological bed in the gravel healthy, while drawing waste down into the bed where it can't be seen floating about, and can be transferred into harmless nitrate. When you clean the tank (removing your 10% water), you just vacuum the gravel by pushing the vacuum tube down through the gravel against the plates. This cleans the gravel and pulls waste out from under the plates too. Draw that dirty water into a bucket and discard...then top off the tank with fresh water that has been treated to remove chlorine, etc.