Al-Nawawi (may Allaah have mercy on him) said in al-Tibyaan:
The scholars (may Allaah have mercy on them) said: The best is to read it in the order in which it appears in the Mus-haf, so he should read al-Faatihah, then al-Baqarah, then Aal ‘Imraan, then al-Nisa’, until he ends with Qul a’oodhu bi Rabbi l-naas (Sooratal-Naas), whether he is reciting it in prayer or otherwise. It is also mustahabb, if he recites one soorah, to recite after it the soorah that comes after it. So if he recites Qul a’oodhu bi Rabbi l-naas (Sooratal-Naas) in the first rak’ah, he should recite from al-Baqarah in the second.
The evidence for that is that the order of soorahs given in the Mus-haf is for a reason, so that order should be followed, except in cases where it is narrated that there is an exception, such as in Fajr prayer on Friday, when Alif-Laam-Meem Tanzeel (Soorat al-Sajdah) is recited in the first rak’ah and Hal ata (Soorat al-Insaan) in the second, and the Eid prayers when Soorat Qaaf and Soorat al-Qamar may be recited.
If he recites them in a different order and recites one soorah then recites a soorah that comes before it, or he recites a soorah that does not come straight after it, that is permissible, even if he is not doing what is best.
As for reciting a soorah from the end to the beginning, there is no dispute that this is not allowed and is blameworthy, because it is a distortion that detracts from the linguistic miracle of the Qur’aan and goes against the wisdom behind the order in which the verses appear.