Later you will need more then 2 channels, maybe an electric sailplane. add ailerons and you need 4 channels. It depends on your budget, but I'd recommend a 2.4 Ghz with at least 6 channels and you don't have to buy another radio for a long time.
To your questions - the radio should have at least the amount of channels the planes calls for.

Mode 2 is the most common radio version in the US, means the left stick is not self-centering and used for the throttle or pitch on a helicopter.
You'd use only the right stick for a 2 channel sailplane.