X-men Days of Future Past: Saw it. It wasn't quite what I was expecting, but still decent. One problem though was the Bluray we were watching it on (or maybe it's the player; hard to say) had moments of skipping so we missed some segments of dialog.
I think the logic with Wolverine is that he's already got his hands dirty and there's no erasing that. He's been in multiple wars, so he's doubtless taken many lives. Raven, by contrast, as they said never took a life, so she's still "innocent" which is the difference. Also the whole butterfly effect situation, yada yada yada. Additionally, the other movies do demonstrate that he is kind of a low life, but he's got some sense of morality.
Also possible the guys he killed he remembers killing in the past anyway, and he did try to avoid it, but eh, so it goes.
As far as seeing other X-men movies go? First 2 are worth watching (or re-watching if you want to remind yourself?), as is 1st Class. X3 is bad, and DoFP really comes off as "excuse to delete X-men 3 from the continuity because we did a lot of unrepairable damage otherwise!" to give you an idea of the kind of errors that movie has. Even ignoring the continuity thing, movie is just all over the place with idiot plot syndrome at times, and even things like "we're introducing this plot element and character! ...now it's dropped until the very end because shut up." Origins is pretty much awful after the first 40 minutes which are good but not excuse enough to watch the movie. The Wolverine, by contrast, is "Good but skippable." The movie was clearly made as a fun hold over until DoFP came out, and it succeeds at that, while having some surprisingly good character work at times (though does seem to have this issue of "Oh crap, we went 10 minutes without a fight scene, FIX THAT NOW!" and yeah, the movie does suffer.)