Parentheses vs. double commas vs. dashes to provide additional detail

(Nitpick: the plural of 'parenthesis' is 'parentheses'.)

Parentheses are used for digressions - things that could be completely removed without affecting the meaning.

Commas and dashes are for setting off clauses that, while not vital to the meaning, serve to provide a fuller picture. Which to use depends partly on the length of the clause—for example, if the clause itself contains a comma, you kind of have to use a dash—and partly on its importance: at least in my perception, a comma-delineated clause is more important to understanding the meaning than a dash-delineated one.

Of your examples, I'd use a comma for these:

• The suspect, Tom Wilson, is now being charged with murder.
• John Smith, a member of the jury, agreed with the verdict.

I'm not sure about this one, but I'd lean toward commas:

• The first example, the one about the fox, is the more valid one.

I'd almost certainly use parentheses for this one, or at best dashes.

• The children (who are wearing shoes) will go on the trip.

I've always felt like parenthesis should be used to provide details which are not "directly" related to the meaning of the sentence. In other words, what's between parenthesis can be ignored without jeopardizing the meaning.

For your first example (Tom Wilsons), I think it depends more on the context: In the current text, are they more than one suspect? If yes, I think double commas are more appropriate.