Interesting question, I'm not sure how to answer it. I think 1 is a pretty tough sell these days, it has a pretty great core story and world building surrounded by a LOT of tedium and fairly bad combat. 2 and 3 are probably still palatable but they tie pretty strongly into the events of the first game that you'd be doing a disservice to yourself by jumping in the middle of the trilogy. That and they don't exactly wrap up in a very satisfying way.
I think they're some of the best games ever made honestly, but as a whole package the original trilogy has some pretty rough edges. That said, I'm not sure ME:A is the best intro to the series either, considering that it also is banking on fans' familiarity with the series.
I'd say if you enjoy space-opera sci-fi then pick up Mass Effect 1, and if you're grabbed by the story, setting, and characters then set the difficulty to normal or easy and don't worry about completing all of the side quests (maybe do a few of the mako ones just to experience how bad they are, but don't bother going for 100%). If you mainline the story it isn't too long of a game and it's worth the experience. 2 feels leaps and bounds more modern in its structure, gameplay, and cinematic quality so it'll feel like a nice treat after completing 1.
And then 3 is...well, it's worth seeing how the story finishes at least. It's pretty controversial for a reason though.
Then by the time you're done with all that, ME:A will be patched and discounted and that'll probably be the perfect time to jump in.