Definitely just get the vanilla trilogy and all of the DLC, and play them 1 > 2 > 3. I would strongly advise you to get them from sources one cannot mention, because virtually every real store offers an incomplete deal spoiled by DRM and shitty business organization.
Its awesome. I wouldn't directly dive into the HD versions/remasters, in the end its just ME anyway.
Yeah ME1 > ME2 is quite a switch, but eventually you will discover that most if not all of the capabilities you used to have are still there and even still segmented in quite the same way. There's just a lower amount of blocks to fill, really, and more things to specialize towards.
Story of 3 and endings... I've never really been inclined to agree on that. There are 3 choices, yes, and they're all suboptimal, but perhaps that's exactly what the game wanted to leave behind. Throughout all three episodes of the trilogy you ARE literally fighting the impossible.