What is the smallest sensible transaction?
I personally think that the most smallest and sensible transaction is at least 0.0001 

HOWEVER NOTE: If you want a confirmation in 10 or 20 minutes, you will need to post a minimum transfer fee of 0.0001 

So technically If you want to transfer 0.0001 to a account you will need at least 0.0002

If you want to transfer a bigger amount, the transaction fee will not need to be changed
e.g. If you want to transfer X amount to a account you will need at least X amount + 0.0001

I have tried to transfer 0.00005593 with no transaction fee, and there is still no confirmations: https://blockchain.info/tx/15ee5484920eed92457643a1709629d8ff579b15fc805b0060a9cf0efdcbb8ed  

Transfer More faster = Pay a Higher transfer fee

Just to note: transfer fee same as Miners Fee same as transaction fee