play ME2... it was game of the year 2010 for a reason.

You would be missing out on some pretty major world building missions that are heavy focuses in ME 3. For example the Krogan Genofage and Quarian Geth Conflict, as well as character building for characters you do like. Skipping it would be a big mistake in my mind.

I would say the better idea would be to play ME2, skip ME3, if you were going to skip an ME game.

As far as the story is concerned, #2 is completely skippable. You can summarize the major points in a few lines, which they do in #3, intermixed in game as you go.

As far as gameplay goes, it was a game of it's time. It's going to look and feel a little dated now. It has a fair amount of jank in some of the movement animations and scripting - easy to get popped up onto railing and not be able to get down, scripting triggers fail, some other weird collision stuff.

If you're only concerned with what happens to the reapers and the galaxy, sure. However, the most emotional moments in ME3 will be very lost on you if you don't see what plots ME2 starts and build attachments to the characters involved. You'll only get half the picture of the first two "acts" essentially. I would not recommend playing 3 without 2. The plot lines that 3 finishes from 2 are the best parts of the game in my opinion.