The most common mouthpieces in use for euphoniums are made by Wick, Bach, and Schilke. I personally like the Wick 4A because it has an open, singing sound. However, as you sound gets more open, you will hear a little more "fuzz" close up. From the audience's seats it should not be a problem. For large shank, the model is 4AL; for medium shank it's 4AM; and for small shank it's either 4AS or 4AY (same thing).

There is also a line of mouthpieces by Wick that are made to Steven Mead's specifications. The model numbers for these start with SM. The Mead SM4 is a fine mouthpiece. It is not suited to all euphoniums because the Mead only comes in a large (bass trombone) and medium ("European euphonium") shank. If your horn has a small shank (like a tenor trombone), then they won't work.

The Schilke mouthpieces (most popular is the Schilke 51D) are more closed, tighter sounding, and don't seem as much like real euphonium mouthpieces to me. They work much better for trombone. However, many people choose the Schilke, including Brian Bowman.

You could also get a Bach 4G or 5G. They both sound better than the very popular 6-1/2AL. The 4G is similar to the Wick 4AL, but is not quite as open sounding. The Bach 5G sounds in between the Wick 4AL and the Bach 6-1/2 and will give you a better high range (at the expense of the fuller sound of the 4G).

I like the feel of gold plating a little better than silver, but it wears out too quickly so I now use silver.