How fast internet needed for AirPlay

I am thinking of buying Apple TV for Airplay Mirroring from my MacBook Pro and iPod Touch 5th gen purposes only. Like i want to play games on my mac but have them also on the TV on a bigger screen. But my internet connection is only 25 KB/s. Once a month it is 200-400KB/s, but that only happens for 4GB of data which i use pretty quickly. Please dont tell me how crap internet it is, i already know. I know that it is wayyy to slow for interent streaming, but when its on a local network only about 15 meters away, will i still be able to have no-lag streaming to Apple TV from my Mac? My MacBook Pro is not Retina it is from 2010. And my iPod is iPod Touch 5th gen. If it is too slow, i will have wasted $110, so please dont just guess give an educated answer. Thanks.