In the Insert | Reference | Footnote dialog, you can select the asterisk,
dagger, double dagger, section symbol series for "Number format," but this
selection will apply to at least an entire section. The most effective way
to use these symbols would be for substantive footnotes when most of your
source documentation is provided by numbered endnotes; that way the
footnotes and endnotes have different reference marks. Any given footnote
reference can be repeated by using Insert | Reference | Cross-reference to
"Footnote number (formatted)."

Footnotes to tables usually appear at the bottom of the table (which won't
necessarily be the bottom of the page). These are best inserted manually.
It's conventional to use the asterisk/dagger series for text tables and
superscript letters (a, b, c) for footnotes to tables that are primarily
numbers.