Wikipedia will tell you that there are two types of parsley: curly leaf parsley and Italian/flat parsley. In Lebanese cuisine, however, I have only seen one type of parsley so far, namely Italian/flat parsley. Although many restaurants may serve tabbouleh with curly parsley, using Italian/flat parsley gives the salad more aroma. And although curly parsley is more decorative, Italian/flat parsley tends to soak up sauces better than curly parsley, making the salad juicier and tastier.
When buying Italian/flat parsley, I usually rely on the herbs’ aroma rather than on its appearance as Italian/flat parsley can often be confused with coriander (also called cilantro). At the supermarket, make sure to read the labels carefully and select parsley, not cilantro.
How to chop parsley and similar herbs? In Lebanon, one does not cut off each leaf from its stem, because the stems contain much of the herb’s taste & aroma. We usually keep the leaves on the stem and regroup all the leaves into a small bush, as shown below.
It is then easier to chop the leaves and the thiner stems into small pieces. You can disregard the larger stems.