I personally wouldn't use a sponge from another tank - if there are any problems in the other tank, bacteria, etc, could be transferred over.. even something that don't both adults could bother the fragile fry.
But that is just my paranoia :)
I use small tubs for my breeding.. here is my latest one. I got a few clear ones though to make seeing eggs/fry a bit easier. I do drill (or use something sharp) to poke semi small holes in the sides (6-8 holes all together) to help keep the water in the container and out of the container the same, so when it's time to transfer them into the tank they don't need acclimation as much.. I'll remove some water from the tub and into the tank, then place some water from tank to tub prior just in case. I keep the sponge filter (on low) during the whole process as the tub stops current from reaching the eggs/fry. I only will transfer the fry once they are free swimming.
In the breeding tub itself I just toss in an IAL leaf, will place live floating plants (from the tank) into the tub once the fry are born - but it's not needed if you don't use infusoria.