I'd like to know what the best diode for this circuit would be (or HOW to pick them. The source is 12volt AC 1amp wallwart. I'd like to be able to pull most of that 1 amp.

 

You can buy them anywhere. I like to buy complete diode bridges as components, just one component with 4 leads.

The things you need to worry about is max current and PIV (Peak Inverse Voltage). With the specs you named almost all of them will work.

You don't say what part of the world you're from, if there is a Radio Shack near you they have them.

 

Like Bill mentions, full-wave bridges are the easiest way to go.

If you have a Radio Shack store nearby, they should stock this part:
http://www.radioshack.com/product/index.jsp?productId=2062581
which will be adequate for your needs.

Two AC inputs, + and - outputs.

The output will be rippled DC, about 15.5v under light load.
If you want to smooth out the ripples, use an electrolytic capacitor rated for 30v or more, about 2,700uF. You could use three 1,000uF caps in parallel.

If you want to be able to regulate the output voltage, you could use a voltage regulator like an LM317 and a couple of resistors to set the output voltage, or a fixed 78xx series regulator. You will lose about 1.7v across an LM317, and about 2v across a 78xx series regulator.