For the Knoxx DLC I'd go with the Siren but I have also done it sucessfully with the Soldier. Others have had luck with the Hunter though I've yet to see anyone do it with the Beserker.
To get the most trophies without changing characters I'd go with the Siren as that will only leave you with 3 trophies for the
. I'd get Moxxie done first as it's by far the most BORING DLC of the lot followed by Claptrap's New Robolution (Only do the Claptrap DLC after finishing Story Mode once).