What kind of airstone should I use?

While most any airstone will work for our purposes, there are a few things to keep in mind.

First, an airstone which puts out very fine bubbles will saturate the nutrients with the highest levels of oxygen moreso than an airstone which puts out larger sized bubbles.
The more oxygen, the better, so choose an airstone which will put out the finest bubbles.

Second, in regards to airstone size, you can choose from the small 1" airstones to the large 6" airstones.

They will all work, and of course the smallest are the cheapest. While its not absolutely critical where the airstone is placed, it is important that it is in the deepest level of the bucket to ensure that long roots are getting enough oxygen.

The small 1" airstones will need to be weighted down with a small lead fishing weight or a nut to keep it at the bottom of the bucket. For this reason,I prefer to use the 4" airstones.
They put out the same size bubbles as the 1" airstones, but have enough weight to them that they will stay placed at the bottom.

 Airstones that sit in the nutrient solution may eventually become clogged, so keep an eye on them. If they do start to clog, you can scrub them with a wire brush under hot water and they will be able to be used again.
To ensure that your airstone is working efficiently, replace them from time to time as needed.