Mesilas Yesharim is written as steps in a ladder. Meaning, you have to work on every attribute before going on to the next and when you do, you reach a new level.
In regard to the order of learning his other seforim I say as follows. In the introduction to Mesillas Yesharim, the Ramchal talks a lot about Olam Haba as mans goal. In Derech Hashem, he goes(among many other things) into much greater depth about Olam Haba and all its details. Therefore, learning Derech Hashem before Mesilas Yesharim can be very hard, since you don't have the foundation (Mesillas Yesharim) of which to build upon. Therefore, it seems to be recommend that one learn Mesillas Yesharim before Derech Hashem.
Also see here that Derech Hashem presents only conclusions to concepts elaborated on in his other works.