What Arduino item I should choose for sending Pressure data to a Mobile?

Sorry if this has been already discussed in previous forums, but I did not find a clear answer.

Is the Arduino BT better choice to buy comparing Arduino Uno + separate Bluetooth device (Arduino Stackable Bluetooth Module)? I have not used before Bluetooth, so can Arduino BT connect in the same time to computer and mobile or is it done one at the time?

I'm planning to have two pressure sensor data transferred to mobile phone. Can some other Arduino item do the work as well (Arduio Nano or Mini)? As saving space would be nice.

Thanks for the help. When I have bought the items... I'll have surely questions about the programming itself.