Get your new tank, fill it with dechlorinated water and get the water up to the right temp and the filter running. Add your new sand / gravel. Then bag your fish. Add all the decor from their previous tank gravel, plants etc and the filter from their previous tank, then acclimatise them and add them to their new home. If you want to use a new substrate just fill the leg of a pair of tights with old gravel and lay it on top of the new (you can remove this after a month) .Run the old filter next to the new for about a month then you can remove the old filter and the new one should be cycled. Of course doing it this way you wouldn't be able to add any more fish until the new filter is cycled as it will only be able to cope with the fish you have.
You could either wait a month then take the old filter out, put it back in the 15 gallon and add the goldfish or you could use the same method with the goldfish running it's old filter until you can put the original back in.
I did this when i moved house, i bought new juwel tanks i moved all my fish from my 29 gallon into the rio 400 which is more than 3 times the size, and all my fish from my 15 gallon into my vision 180 which is nearly three times the size.
Starve your fish for a couple of days before bagging them and they won't produce as much waste.
Emma