I'm taking undergraduate studies in Social Sciencies and because of a research I'm working on I started to read Merleau-Ponty's Phenomenology of Perception and realized that this book requires a certain amount of previous knowledge on Phenomenology. So I thought about reading Cartesian Meditations: An Introduction to Phenomenology from Husserl. Is it a good start on the field of phenomenology? If not, what book do you suggest?
Alp Uzman's answer is great, Robert Sokolowski's Introduction to Phenomenology is truly second to none resource for beginners. It describes nearly all Husserlian methods and terms. You should definitely start with that, Sokolowski is a great Husserl scholar. His introduction is a general introduction to Phenomenology from mainly Husserlian perspective.
Another great scholar that dedicated his whole life on studying Husserl is Dan Zahavi. Thus, I recommend his Husserl's Phenomenology as a secondary read before embarking on Husserl himself.
Lastly, after you read some of Husserl's works, for Merleau-Ponty I suggest to follow Hubert Dreyfus' (another great scholar) syllabus for the introductory study of Merleau-Ponty's Phenomenology. It basically involves prerequisite of doing John Searle's video course on Philosophy of Mind and then read Phenomenology of Perception along with his series of 31 lectures on the book.
My humble suggestion would be Robert Sokolowski's Introduction to Phenomenology. I haven't read Moran's introduction, but a quick look at the contents suggests he chases names and texts.
Sokolowski's introduction instead is light on names and the differences between flavors of phenomenology and surveys basic ideas and methods. In this regard Sokolowski's text might be considered more elementary than that of Moran's. It also has a "further reading" section at the end, which includes suggestions on Merleau-Ponty's work. As a disclaimer I remember mostly non-intrusive religious threads every once in a while, which is a pro or a con depending on one's convictions.