How do I study Shafi'i Fiqh on my own, by way of understanding or memorization, so that I may know the rulings and apply them to myself?

There is no contradiction between memorization and comprehension in seeking knowledge. Comprehension is the objective of knowledge, and memorization is a means to solidify understanding and protect it from oblivion.

Knowledge can be acquired through two ways: First, receiving it from reliable books. This requires considerable time and effort and may lead to weak understanding and errors. Second, receiving it from a reliable scholar (shaykh) in his knowledge and religiosity. This is faster, more precise, and opens horizons in understanding and verification. Combining both methods is the most complete.

Among the most famous concise texts for beginners in Shafi'i jurisprudence are "Mukhtasar Abi Shuja'" or its versification, and "Matn Az-Zubad" by Ibn Ruslan. After mastering these texts, one can move on to "Al-Minhaj" by Imam An-Nawawi.