All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Reciting some portions or verses from the Quran after Al-Fatihah in the first two Rak’ahs of the prayer is a desirable and not obligatory Sunnah, according to the view of the majority of the scholars for the Hadeeth of Abu Hurayrah who said: “Recitation (of Soorah Al-Fatihah) in every (Rak'ah) of prayer in essential. (The recitation) that we listened to from the Messenger of Allah, we made you listen to it. And that which he recited silently, we recited it silently as well (and we did not recite it loudly). And he who recites Umm al-Quran (Al-Fatihah), it is sufficient for him (for the validity of the prayer), and he who adds to it (recites some other verses of the Quran along with Soorah al-Fatihah), then this is better.” [Ahmad and Muslim]
The least that is acceptable to read [i.e. after Soorah al-Fatihah] is one verse, and Imam Ahmad preferred that it be long, like the verse of debt [Quran 2:282] and Ayat Al-Kursi [Quran 2:255] But if the worshiper recites only one verse, then it should provide a meaning or a ruling on its own, because some short verses such as verse مُدْهَامَّتَانِ) ({Dark green [in color]} [Quran 55:64] does not provide a meaning on its own. Al-Bahooti stated this in Kash-shaf Al-Qina‘a.
Based on the above, you should know that it is neither obligatory to recite Soorah after Al-Fatihah, nor to recite three verses. As for the length and shortness of the verses, it is according to the number of their words and letters. Among the long verses are the verse of debt [Quran 2:282] and Ayat Al-Kursi [Quran 2:255]; and among the short verses are مُدْهَامَّتَانِ) ( {Dark green [in color]} [Quran 55:64], and (ثم نظر) {Then he considered [again]} [Quran 74:21]
Allah Knows best.