guppies, get one. Several hardware/ big box stores have plastic ones on sale now and they "seem" pretty safe. (I'm up to 10 buckets. This makes it easy to trip anywhere in the house or yard.)
First rinse out almost enough gravel (outside) to line the new tank to a depth 1 inch/2.5cm. That is roughly a pound or .45 kilograms per gallon/ 4 liters. When the dust of that is gone, place it in the new tank (and congratulations on the new tank!) There is even an Immediate Help entry on gravel washing.
Don't let the gravel dry. If time will be needed to do the stuff below, put a gallon of seasoned, treated water in with it.
Then take the top five gallons/19 liters of water out of the first aquarium, maybe gently siphoning it into the bucket. Catch and put the guppies in that bucket.
Then take a net and run it through the gravel still in the tank, shaking the dust and gunk out. Assuming that it is sort of clean (doesn't smell) place it on top of the new gravel in the 20 in order to kick start the nitrogen cycle. Nuts, you are going to drip from the net unless you get a second bucket. ;)
Put the five gallons of water in the new tank. Gently pour some of it into a soap-less glass cereal bowl or small pickle jar. This hopefully will keep the gravel from being too stirred up.
When a certain amount of the water is in there, take the now traumatized guppies out of the bucket and put them in the tank. Complete the transfer of water.
If you have a box or sponge filter in the smaller tank, rinse the gunk out of it and move it (still wet) to the new aquarium. That is another boost for your new nitrogen cycle. :)
Now since you are such a good planner, you will have been saving some gallon water jugs with treated, seasoned water of about the same temperature as the tanks. Add about 4 gallons gently to the tank.
There is no law which says that a new (or established) tank must be full. That is easier done if you don't have a HOB (hang on the back power filter). Add 3-4-5 gallons of water a day until it is as full as you want it.
Then you can use some water and gravel and a filter to recolonize the smaller aquarium. ;)
Thinking of full tanks... if you have fish which jump, make sure the tank is completely covered. Or run it a few inches from full.
That old tank will be excellent as a quarantine/ hospital tank. Other uses will come to mind. :)
Good luck and have fun!