"NEW_SELECTION" actually refers to the selection type. Selection types include:
NEW_SELECTION —The resulting selection replaces any existing
selection. This is the default.
ADD_TO_SELECTION —The resulting
selection is added to an existing selection if one exists. If no
selection exists, this is the same as the NEW_SELECTION option.
REMOVE_FROM_SELECTION —The resulting selection is removed from an
existing selection. If no selection exists, this option has no effect.
SUBSET_SELECTION —The resulting selection is combined with the
existing selection. Only records that are common to both remain
SWITCH_SELECTION —Switches the selection. All records that
were selected are removed from the selection; all records that were
not selected are added to the selection. The Expression is ignored
when this option is specified.
CLEAR_SELECTION —Clears or removes any
selection. The Expression is ignored when this option is specified.
To get the results of one tool to be used as the input for another, you will need to mark that output as a parameter (right click-->check Model Parameter)
If you need the outputs of your model tool to appear in the Results
window, you must make those outputs model parameters. For example, if
your tool outputs an HTML file and you want the user to be able to
click on that file from the Results window you must make the HTML
output file a model parameter.
More on Model Parameters - ArcGIS 10