The only real difference between mysql_fetch_row and mysql_fetch_array is that mysql_fetch_array allows you to retrieve the value using either the index or the fieldname. for example based on what you wrote you could do either of the following.
echo $FieldValues["FieldName1"];
echo $FieldValues["FieldName2"];
or
echo $FieldValues[0];
echo $FieldValues[1];
while using mysql_fetch_row you would have to use the index.
echo $FieldValues[0];
echo $FieldValues[1];
using the array method consumes additional server resources, however these are negligable and therefore not a real factor in the decision. If you have no plans or interest in using the actual field names then "row" is probably the best practice. However if there is anychance you may use the field name then go ahead and use "array".
Hope that helps,
Richard