Hello Mark. For traditional, classic American-style pancakes, standard all-purpose flour (often labeled simply as AP flour) is the absolute best and most reliable choice. This is almost certainly what your mother used.
To help you understand why, here is a quick breakdown of what you saw on the shelf:
All-purpose flour has a moderate protein content, usually between 10% and 12%. This provides just enough gluten structure to hold the trapped air bubbles from your leavening agent, resulting in pancakes that are soft, fluffy, and sturdy enough to flip without falling apart.
Pastry flour has a lower protein content (around 8% to 9%). It makes exceptionally tender pancakes, but they can sometimes lack the familiar body and height of classic diner-style pancakes.
Self-rising flour is just all-purpose flour that has already been blended with baking powder and salt. While convenient, it limits your control over the leavening and seasoning of your batter, and leavening agents in premixed bags can lose their potency over time.
To ensure your pancakes do not turn out dense or heavy with all-purpose flour, here are two gentle recommendations: first, whisk your dry ingredients together with standard baking powder, a pinch of salt, and a little sugar before adding the wet ingredients. Second, mix the wet and dry ingredients just until combined. It is completely normal and desirable to have lumps in the batter. Overmixing develops excess gluten, which is the primary cause of tough, rubbery pancakes. Allowing your mixed batter to rest on the counter for about 10 minutes before cooking will also make a noticeable difference in fluffiness.
I hope this helps you make a wonderful breakfast for your family.