Play 1, 3, and 4. Play 2 only if you feel like seeing how bad it was in comparison.
If you play the PS2 version of DMC1, the controls are really weird (jump is Triangle for example) and the NA release was made harder than the Jap or EU release. Dante does 20% less damage and takes 20% more damage. However, the HD collection version of DMC1 is just a re-translated Japanese version, meaning jump is X where it is supposed to be, and it's easier because those damage changes aren't present. Sadly there are some minor bugs with the HD release, but they shouldn't really be a problem (stuff like background ambience sounds not looping correctly).
The original PS2 release of DMC3 once again made the NA version more difficult. This time they took the Japanese "Hard" mode and labelled it "Normal" instead. If you play DMC3 Special Edition (PS2 or HD collection) then you get the proper "Normal" difficulty back.