Imam Suyuuti in his book الإتقان, mentioned four sayings as regard the first Verse/Surah revealed by Allah.
The First Saying: The first five verses of Suratu ‘Alaq. And the evidence of this is the famous hadeeth of Aaisha radiya Allahu anhaa that says the prophet was in the cave of Hira when Jibreel came and said to him “read” and the first 5 verses were revealed, then he went to Khadeejah radiya Allahu anhaa to cover him up…. Till the end of the hadeeth.
The Second Saying: The first Verse revealed was يا أيها المدثر , قم فأنذر (Qur’an 74 verse 1: 2).
The evidence for this is the hadeeth narrated by Yahya bn Abee Kathir. He asked Abu Salamah bn AbdirRahmaan about the first Verse Allah revealed, he answered: ياأيها المدثر, I (Yahya) said: “people are saying it is إقرأ باسم ربك الذي خلق” Abu Salamah said: “I asked Jaabir bn Abdillah radiya Allahu anhumaa about that, and I said to him exactly what you said, then Jaabir said: I will only tell you what the Prophet told us, the Prophet said “…. I was called, I looked at my right side and I couldn’t find anything, I looked at my left side and I couldn’t find anything, I looked at my front and I couldn’t find anything, I looked backward and I couldn’t find anything, then I looked up and I saw something, I went to Khadeejah and said to her “cover me up دثروني, pour cold water on me, I was covered up with clothe and cold water was poured on me, then Allah revealed يا أيها المدثر, قم فأنذر..”
The Third Saying: Suratu Faatihah.
Those who opine Suratul Faatihah was the first to be revealed presented the hadeeth recorded by AlWaahidiy from Abu Ishaaq, from Abu Maysarah; the Prophet, whenever he heard someone calling his name (O Muhammad يا محمد), if he heard a voice, he would ran away frightened, Waraqah bn Nawfal then said to him: “whenever you heard a voice, stay and listen to what the voice is saying to you” the prophet later heard a voice called his name again, and he answered “لبيك here I am!” the voice said “say Ash-hadu an Laa ilaaha illa Allahu wa Ash-hadu anna Muhammadan rasoolu Allah” and say “Alhamdulillah rabbil aalameen, Ar Rahmaan Ar Raheem… Till the end of Suratu Faatihah”. This hadeeth is Mursal.
The Fourth Saying mentioned by Imam Suyuuti is “Bismillah Ar Rahmaan Ar Raheem”.
And all these four sayings mentioned by Suyuuti are all what those who have authored books on Uloomul Qur’an after Suyuuti also mentioned. Only that we need to stress that some of these sayings are weak.
As for “Bismillah Ar Rahmaan Ar Raheem” being the first Verse Allah revealed, this saying is weak. And Imam Zarkashiy whom was one of the Major references of Imam Suyuuti in his book الإتقان did not mention this saying in his own book البرهان. Also, there is no authentic and connected narration that says Bismillah Ar Rahmaan Ar Raheem was the first Verse revealed; because what is known is that, so far a surah is revealed, Bismillah Ar Rahmaan Ar Raheem will be revealed alongside with it.
As for the third saying that Suratul Faatihah was the first Verse revealed, even though the hadeeth mentioned was considered weak, some scholars related the hadeeth to a similar sound hadeeth – which is the hadeeth of Aisha that says the first surah to be revealed completely is Suratul Faatihah.
Some Scholars of old like Imam Zamakhshariy (rahimahu Allah) in his book الكشاف Volume 4 page 223 mentioned that, most scholars of tafseer are of the opinion that Suratul Faatihah was the first to be revealed. Even though we will rather say the majority of the scholars are of the opinion that the first five verses of Suratu Alaq was the first revealed.
As for Suratul Mudathir being the first Verse revealed, if the first 2 sayings discussed aren’t authentic, as for this saying, it has been narrated in Sahih Bukhari from Jaabir bn Abdillah, and the hadeeth is on the same level of authenticity with the hadeeth of Aisha that says Suratul Alaq was the first revealed; so, scholars tried to make comparism between the hadeeth of Alaq and this of Mudathir. Some of them said, Suratu Mudathir was the first Verse completely revealed. Some other said, Suratu Mudathir was the first surah revealed because of an occurrence. Some other said, Suratu Mudathir was the first surah revealed to command الإنذار (da’wah). While some scholars said, Suratu Iqraa was revealed to establish the prophethood of the Prophet, while Suratu Mudathir was revealed to establish his message.
All these interpretations of comparism, not all of them are correct; some are arguably. As for the saying that Suratul Mudathir was the first surah completely revealed, this is not true. This is because, it was recorded in Saheeh Bukhari that the first part of Suratu Mudathir revealed was verse 1 to 5; and if we claim Mudathir was the first to be completely revealed, Islam rulings were legislated one after the other (stage by stage), and verses 11 to 31 of Mudathir are telling threats and punishment of those who disbelieve after dialogue; it is highly not correct to say these verses are the first revealed in the early stage of da’wah when the Prophet was yet to call them to oneness of Allah.
And there is another narration from Abu Salamah that Jaabir bn Abdillah was telling them about the period/duration of Wahy and he mentioned therein that the first Verse revealed are verses of Mudathir. This narration, if we take a good look at it, we may conclude that the first verses revealed are that of Iqraa, then the duration of Wahy started afterwards. If we go by this, there will be no contradiction between the hadeeth of Aisha and Jaabir.
You should also note that there are some sayings mentioned about the first Verse revealed that Imam Suyuuti did not mention in his الإتقان. Among these sayings are: the first Verse revealed was Suratu Muzammil; and a saying which belongs to Mujaahid says the first verse revealed was Suratu Qalam (ن).
As for Muzammil, the ahadeeth mentioning that are not established authentic and also, it commands the prayer of tahajjud, which cannot be said to be first revealed in the beginning of Islam.
May Allah grant us the light and guidance of Qur’an.