Cheapest flash for green box

My mother in the last year bought a T3 (not T3i) with the 18-55 and 55-250 lenses. She is using this to take photos of her kids and grandkids. Nothing fancy and she has no aspirations of taking it out of green box mode. The biggest problem with all of this is that indoors, the pop up flash is firing, and of course looks terrible. What is the cheapest flash I can give her that she can put on top and turn on and do nothing else? Will a TTL work or is ETTL required (yeah I don't know the difference)?

I want it to be able to rotate up and down but left and right isn't as important.

Will this work? http://www.amazon.com …K8WH&coliid=I2M​SAR16S7S9G

I've only ever used manual flash so I'm a bit out of my element.

Yes, any model marked ETTL II will do what you want. That seems like a pretty capable flash for the money.

If your main goal is to improve upon the light quality from the pop-up, I highly suggest getting a model that has side-to-side swivel (at least 180° in one direction), in addition to the vertical movement. Bouncing off of something to the side, or behind, or a combo of the two can produce excellent results compared to just bouncing upwards.