Answer
To order the fields differently than the default, or to return only a subset of the available fields, set the return fields list with the order of the desired fields.
v2006 and v2006.1 Spatial Query example:
returnFields = [NAME, CITY, STATE]
v2 Proximity/Query example:
returnFieldsList = [NAME, CITY, STATE]
Example result:
ESRI, Redlands, CA
Note:
Field names are case sensitive. Verify they match the format returned from the method getAvailableFieldNames.