The June 9, 1908 NYT reports that the U.S. Olympic team had been selected the day before in New York City:

Seventy-six athletes were selected yesterday to represent the United States at the Olympic games in London next month. A supplemental list of fifty-eight men has been added to the regular list, and it is probably that many of these will be added before the team sails. The committee wrestled with the selection problem for nearly ten hours at the Astor House before a decision was reached.

How much was it expected to cost for each Olympian?

The minimum subscription which will be accepted to defray the expenses of sending any one entrant to the games was fixed at $325.

In 2006 dollars, this comes to $7,345.

In 2000, the United States spent approximately $400m (in total) for Olympic sports. I haven't been able to track down exactly how much is spent on taking the team to the Olympics, but my guess is that it is considerably more than $7,300 per athlete.

An interesting tidbit is the amount of lobbying by the US Olympic Committee reported by OpenSecrets:

Notice the up-tick in lobbying efforts the year before an Olympics, most noticable before a summer Olympics.