There are some DLC's that you'd want or like.
Mass Effect 1 on Origin has both DLC's included now, so that is covered.
ME2 relevant DLC's: Overlord, Zaeed (you'll get this for free), Arrival (from what i recall this is influenced by one of the DLC's from ME1), Kasumi (short, but brings one of the most interesting trammates in ME2), Normandy Crash Site (free), Lair of Shadow Broker (best of the bunch with repercussions in ME3), Firewalker (replaces the Mako missions, you get this for free).
ME3 relevantd DLC's: you want that Deluxe edition for the extra character and story. Other relevant DLC's: Omega, Leviathan and Citadel. You get the MP DLC's for free + the Extended Cut which expands the endings (also for free).
You can skip weapon packs, appearance packs, the Genesis DLC for ME2 and ME3 (those are for people that don't have the previous game and want to know what happened and make some of the decisions that were available in the previous games).