Transmission for push-button Barracuda

I have the shell of a push-button 64 Barracuda, no engine, no transmission. I have a 318 engine which I would like to put in it. I have heard that I need a 904LA transmission to match the engine. I don't know if that is correct. I also don't know whether that transmission - or any other suitable - would also function with the push buttons. I have only just begun to learn about such things, so please understand my ignorance. Guidance, please!