Setting your number to forward straight through to your number/device without a main greeting is simple.

STEP 1: Change to Ringtone.  

Go to Settings --> Music on Hold, and change to "Ringtone"

STEP 2: Create an extension with the desired forwarding number. 

Go to Extensions --> and click Add Extension.

When adding the forwarding number, make sure the forwarding numbers "Forwarding Options" are set to "Calls will connect to you as soon as you pick up."

STEP 3: Remove the greeting, and forward directly to the new extension.  

Go to Settings --> Your Numbers

Set the simple forwarding number's "Forwarding Options" to "Transfer to extension..." and select the extension you created.