I would recommend cycling a 10-gallon aquarium and once it's stable, moving them then.
My favorite filters are the AquaClear external filters by Hagen. They provide similar filtration to an expensive, powerful canister filter--but are easy to maintain and inexpensive. I also like that they don't rely on a single filtration pad--most hang-on-back filters do and that means changing it will kill off a ton of beneficial bacteria. Plus, having different types of filter media means you filter out more stuff
. Whisper filters are alright but I don't like them for frogs because they're not too adjustable and tend to be too strong. They aren't too customizable, either, when it comes to filter media.
Set the tank up, filter included, and either add Tetra SmartStart (previously called BioSpira) or start "feeding" the tank small amounts of food and let it cycle itself. You want beneficial bacteria to grow so that they can convert ammonia into nitrite and than nitrite into nitrate (nitrate is fairly safe compared to toxic ammonia and nitrite). The nitrate will be removed through partial water changes/gravel vacuuming. If you use the SmartStart, the frogs can be added right away because you're literally pouring in bacteria. If you cycle the tank yourself, it may take weeks before it's safe (or it could take days, it depends). While feeding the tank, test the water daily to see how far along you are. First you'll have an ammonia spike (caused by the rotting food) but once bacteria become established, ammonia will go down and instead you'll find nitrite. Once your ammonia and nitrite are at zero and you instead are finding nitrate, do a small water change and add the frogs. Partial water changes will be all you'll need now, there's no need to clean out the whole tank or worry about ammonia spikes. Test the water regularly at first, though, just to make sure everything's ok.
The thing is, doing full water changes with a "larger" (compared to, say, a 5-gallon) aquarium just isn't practical. Besides, cycled aquariums are much more stable and healthier for the animals
. It's usually easier to cycle aquariums if you have some sort of substrate so I would get large, rounded gravel or sand. If you want an easier time getting things stable, consider adding a few hardy live plants such as java ferns.