DA is double action and named appropriately because when you pull the trigger two things happen. hammer is cocked back and then released!
SA is single action and the hammer is already cocked back so when you pull the trigger there's only one action, the hammer is released and the firearm fires!
DA/SA means first trigger pull is DA and the rest is SA until the magazine is out
hope this clears things up a bit
as for the sig i dont own one but i hear good things about it and i've held one before and its feels pretty good in the hand.
i may be little partial but have you considered a 1911?