Tafseer of Qur'an is the commentary or explanation of the verses of Quran. There is generally no overall best tafseer for everyone. The best tafseer is one which fulfils your goal.
For the layperson, I would suggest a simple tafseer of scholars like al-Baydawi or an-Nasafi or al-Khaazin.
For those who read in English only, The Ascendant Qur'an: Realigning Man to the Divine Power Culture by Imam Muhammad Al-Asi. He has a great command of English and expresses his ideas very fluidly. Ma'aariful Qur'an by Pakistani Sunni Islamic scholar Shafi Usmani is also a good English tafseer.
A more comprehensive tafseer includes Jaami' al-Bayaan fi Ta'weel Aayi-'l-Qur'aan by the Persian scholar Imam Muhammad ibn Jareer al-Tabari (838–923). He quotes opinions of earlier generations with chains (isnaads) usually not present in many books of tafseer and includes linguistic and grammatical explanations to many words.
If you want a more detailed or sophisticated tafseer, al-Bahr al-Muheet by Abu Hayyan al-Andalusi would be better; or Mafaatih al-Ghayb (at-Tafseer al-Kabeer) by Fakhr al-Deen al-Raazi.
For someone who wishes to understand the legal injunctions in the verses better Qurtubi is helpful. Whilst his tafseer covers the usual areas of tafseer his commentary on many of the ahkam relating to the shariah are more deeper than usual tafseers.
Zamakshari is great for those wishing to gain a deeper insight into the linguistic aspects of the Qur'an.
Tafheem ul Quran by Mawlana Sayyid Abu al-A'la Mawdudi is a more contemporary tafseer, written over a 30 year period. It is a combination of orthodox and modernist interpretation, deeply influencing modern Islamic thought. It covers debates regarding economics, sociology, history, and politics highlighting a Qur'anic perspective showing Islam provides guidance in all spheres of human endeavour.
Analytical and Research
This section is a little more detailed, aimed at scholars who prefer not to leave any stone unturned in relation to tafseer; I would suggest they review the above-mentioned tafaseer in addition to the following:
There is no overall best tafseer for everyone. The best tafseer is one which fulfils your goal most appropriately. Moreover the Qur'an unfolds its meanings with time so later mufasireen are probably more helpful for contemporary events.
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