Mass Effect 2 DLC questions?

I got ME2 for xbox 360 a week ago, and i want the dlc like arrival, lair of the shadow broker etc. But i havent beaten the game yet, so my question is should i wait until after i beat the game or should i do it before. Also, after you beat the game, are you allowed to continue exploring, or does it just end? I want to know so i can know if i should wait until the end of the game to get the dlc. I could just load up an old save though.