For YDNA, if you tested your father, there is no need to test yourself.
If by highest level you mean 111 markers, fine. Otherwise, if you tested
for 37 or 67 markers you can still upgrade his test to 111 markers. This
will serve to narrow down his match list and put a "most recent common
ancestor" within fewer generations.
For mtDNA, if you tested your mother, sibling or maternal uncle/aunt,
there is no need to test yourself. As your mtDNA was passed down by your
mother, if you want to investigate your father's maternal line, you can
test or upgrade your father's sample for mtDNA. The highest level here
is the mtFull Sequence.
As for atDNA, if you tested both your parents there is no need to test
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