iMessage only works if your phone has an Internet connection at the time of the text. This means that if you have no Internet connection, your text will be sent as a SMS message, instead if an iMessage one. However, if someone else with an iPhone texts you when you don't have Internet, you will receive it as an SMS message. You only send and receive iMessages when both of you are connected to wifi.
When you turn off your 3G, roaming, and data streaming, you can only receive messages via iMessage with wifi. If you completely turn off wifi and 3G (as in putting your phone in airplane mode) you cannot receive any texts at all. Turning your phone off will also prevent messages from coming in.
There is no prompt option to send a message via iMessage or standard SMS, it is done automatically based on your wifi connection. As a tip, iMessage messages contain blue text bubbles, while SMS messages are green.
Also, I would check your iMessage settings to verify that you are able to recieve messages with your phone number, rather than just with your Apple ID. If you don't have your phone number set up to recieve, then you will not be able to recieve them as texts.