Just a few months out from Mass Effect: Andromeda, EA has put Mass Effect 2 into their “On the House” promotion. As usual, this is a temporary 100%-off sale; if you get it, then it’s yours. All you need to do is log in to the Origin store, browse the “On the House” sub-section of Free Games, and add it to your library. I’m sure EA would like you to install it and get hooked on the franchise as soon as possible, but you can just leave it there for a while if you’re busy at this point in life.
Mass Effect 2 is generally considered to be the best in the series, at least thus far, so it’s both nice and logical that EA would choose this one for the promotion. The first one had a few technical issues, and it was also the introduction to the series; the team could see what worked and what didn’t, and have the confidence to add new mechanics and so forth. Also, it was apparently designed to be welcoming to players who missed the first game.
Personally, I tried the first Mass Effect but had to reformat my PC before I got more than a couple hours into it, and I never really installed it again. This promotion might be a good excuse to get back into them if I can spare a little time, which, for Mass Effect, means quite a bit of actual time.