Basically the way this works is there is a set of characters in the original movies, and then there are some younger versions of the characters in the First Class movies (except for Wolverine, who remains a constant). I like the X-Men First Class (younger versions) sequence better. I find the movies funnier, more clever and with more interesting character dynamics. I also appreciated the Star Trek callouts.
X-Men (2000) – watch
X2 (2003) – watch
X-Men: The Last Stand (2006) – X-Men 3 – this is terrible. skip.
X-Men: First Class (2011) – X-Men First Class 1 – watch
The Wolverine (2013) – I haven’t seen. Doesn’t have good reviews.
X-Men: Days of Future Past (2014) – X-Men First Class 2 – watch
Deadpool (2016) – I refuse to view this
X-Men: Apocalypse (2017) – X-Men First Class 3 – watch
Logan (2017) – Wolverine 2 – Supposed to be good, but harrowing. I haven’t seen.
The timelines of the two overlapping X-Men can be a bit confusing to sort out.
First Class is in 1962.
Days of Future Past is in 1973 (mostly).
In my opinion, Days of Future Past alters the future so that the terrible The Last Stand never happened. In Days of Future Past they also make it look like Mystique is saving Wolverine from Stryker, but clearly he is eventually captured, because we see him imprisoned in Apocalypse. (Presumably they had to do this to keep some integrity in the timeline.)
Apocalypse is in 1983.
It’s not clear to me exactly what years X1/2/3 are set in. Looks like they are more or less set in their release years, sometime in the early 2000s.
More movies are coming of course. The next one in the First Class sequence is apparently Dark Phoenix.