What is the best order among the tafsirs of Ibn Kathir, Al-Tabari, and Ibn Abbas, and how should I deal with the difference in interpretive methodology between Ibn Abbas (who focuses on the reasons for revelation) and other tafsirs (which focus on the general meaning)?

Ibn Kathir's Tafsir is the best for a beginner student because of its focus on Tafsir bil-Ma'thur (interpretation based on tradition), rulings, interpreting the Quran by the Quran, and mentioning the chains of narration for most of the reports from the Salaf (early Muslims).

Al-Tabari's Tafsir is the first, best, and most comprehensive of the exegeses, due to its attention to various recitations and linguistic aspects, and its narration with chains of transmission from the Salaf. It addresses the clarification of statements, their prioritization, grammatical analysis, and derivation of rulings. The Ummah (Muslim community) has unanimously agreed that nothing similar to it has been authored.

As for the Tafsir attributed to Ibn Abbas, known as "Tanwir al-Miqbas," it is very weak. Its chain of narration (al-Suddi al-Saghir from al-Kalbi from Abu Salih from Ibn Abbas) is known as the "chain of lies," as both al-Suddi al-Saghir and al-Kalbi were accused of fabrication.

There are useful concise Tafsirs for beginners, such as Al-Jalalayn, Al-Baydawi, and Al-Sa'di, for clarifying obscure words and explaining ambiguities.