Electronic – Ipad charging via usb port

An Arduino Uno can be powered by

• a stable (regulated) 5V DC, which you can either supply via the USB power lines, or via the shield connectors, or
• an unregulated 6-20 V DC (7-12V recommended), which you can supply via the 2.1 mm centre-positive barrel plug connector.

I would not recommend using a 9V battery, because its voltage will drop quickly, but in a pinch this can be used.

ref: http://arduino.cc/en/Main/ArduinoBoardUno

You don't need to isolate. If you don't, you do need to tie the grounds of the circuits together if you're using the separate power supply.

That said, while you're doing your development, you might just screw up and do evil things. I recommend using a USB hub until you know that everything is perfect. This way, screwups are more likely to take out your hub than your computer's USB port or motherboard.

You can use either the off-board power supply, or use the USB bus to give you power, depending on how much current you need.

You might also consider why you're doing the project in the first place. If it's super important that you have a very quiet ground, you might opt for isolation. Of course, simply isolating and guaranteeing a quiet ground are two different things.