Buy the trilogy set, and start with the first. Not only is it first chronologically, you won't get spoiled by 2 and 3's combat first.
Also, before starting your first playthrough, install these:
1. Cerberus Pass for ME2 [something to that effect]. it is free now, and it gives you Normandy Crash Site, Zaeed: Price of Revenge, Firewalker Pack, and I think a weapon pack [could be wrong]. Make sure you have those installed before playing ME2 for the first time since they are free and give you more content.
2. Mass Effect 3's online pass and all of the MP DLC's. They are all free and give you the optimal Multiplayer experience.
3. Most importantly, install the free Extended Cut for Mass Effect 3. You will be VERY glad you did. Makes the ending a lot more tolerable.
Then, if you find you really like the games, I'd suggest:
1. Bring Down the Sky for the first Mass Effect.
2. Kasumi: Stolen Memory, Overlord, Lair of the Shadow Broker, and Arrival for Mass Effect 2. Especially those last two, as they are plot important
3. From Ashes, Leviathan, and Citadel for Mass Effect 3. The first two are plot important, and the Citadel one is just awesome, but I won't spoil them.
And if you simply LOVE Omega in ME2 and LOVE the combat in 3 a lot, then I'd suggest Omega's DLC in ME3. It is only worth that $15 pricetag if you absolutely loved the ME3 gameplay.