Just to add a bit and hopefully make it easier.
For jobs like this i.e. LED or some other on/off load don't worry about the gain of the transistor just go for one that will handle the load current that you need.
Gain only really plays havoc when you are amplifying analogue signals and or you need to know the exact relationship between input volts or current and output volts/current in these digital examples of switching on an LED you don't care about distortion, over drive or quiescent points etc etc. All you need to know is put a voltage on the base and the LED will light..hmmm I hope I've made it simpler anyway.