I'm omitting X3, as that movie was crap. So my question is, should I watch the three remaining movies in chronological order (First Class, X-Men, X2) or release order?
Why didn't you like X3? I thought that it was really well made, and stayed in the spirits of the X-Men universe.
X1, X2, First class. My understanding is, and I could be wrong, Days of Future Past is like the sequel to First Class and X2. So if you watch First class first, you're left with an unfinished story for two more films. If you watch it last, X2 and FC provide a double cliffhanger to be finished and connected when you watch DoFP. I don't think you can go wrong either way. As for X3... The movie is a disaster on so many levels. From the story, dialog, etc... I didn't like anything about it. Glad Singer has erased it from X-men history. 93% on Rotten Tomatoes. I told everyone Singer would kill it.
I didn't mind X3. It wasn't a great movie by any means but it's certainly watchable unlike Superman 3 or Superman 4 for example. It had some decent fight scenes and special effects. I think it's better than the two stand alone Wolverine movies, which the new X-Men movie also erases from its history. But to answer the original question I'd go with the release order: X-Men, X-2, First Class.
Watch the post credits scene of The Wolverine. You could watch the whole film, but there is nothing in it that carry forward to DOFP.