Either.
absolutely
This is OK, but it would be more usual to say:
That is absolutely the best way to do it.
than to use the word order you've suggested. I did a
Google battle and got :
absolutely the best - 4,520,000 examples
the absolutely best - 1,650,000 examples
absolute
But
the absolute best brought up 13,300,000 examples. So in wins out over both the others. To me it sounds very informal and emphatic however. So I'd suggest ...
in neutral style -
absolutely the best is usual
more informally -
the absolute best is fine