How do we choose the correct characters for a westerner name?
It's your name and you can arbitrarily pick characters to be your name.

We Chinese generally select characters with positive meanings (of course, I think characters with negative meanings would not be the choice for most people) and avoid possible bad meanings from the words with the same or similar pronunciation with the name.

For example, it's common to see characters like 刚（rigid), 强 (strong), 杰（excellent), 明 (bright), 阳（sun), 洋 (ocean) in a man's name, and 艳 (beautiful, brilliant), 卉 (flowers), 丽 (beautiful), 芳 (fragrance), 静 (quiet) in a woman's name.

Also, some people, will name their offspring after related characters. A good example is the name of the famous poet and politician in Song dynasty, 苏轼; his brother's name is 苏辙. "轼" is the rail on a wagon and "辙" is the track a wagon leaves on the road.

Some people will also select words from classic Chinese books to be the name. trideceth12 shows the name "云龙"; I am not sure whether he takes this word occasionally or not, but this word really comes from the book of "Yì Jīng"(易经),"云从龙，风从虎".