I think the strongest factors here are political and the native language of the linguist that in most cases go together because the linguist should have support from community and government. In another case, the linguist's work will be just an academic exercise.

A few observations.
Only when I started learnign Arabic I learned that there are old books in Belorussian written in Arabic script. Wooden mosques in numerous Belorussian villages (and one demolished in Minsk) were also a surprise. 

I wonder if this is known well in Belorussia.

When the Chinese were developing Yi,  they invented Yi syllabary... Instead of already existing logographic Yi script. Why?

@Val, yes. I think in this case when a certain choise makes the system more likely to be adopted, the author is going to make this choice, whether it is "good" or not. I think in this case it going to be Cyrillic with standard letters of Turkic Cyrillic alphabets and perhaps really minor changes to adapt it to its phonetics. If the community were nationalist, then it would most likely be Latin. Modern nationalists love Latin more than creating new letters or restoring historical letters. P.S. yes, Cyrillic. The discussion is interesting. I liked how the Turkish guy found Latin more natural for a Turkic language:) 

I wonder what would he say if I told that Greek or Armenian is no less natural (especially given that these alphabets are more native to Turkey). 

Kseniia, Chinese demonstrates how many arguments which favour some aphabetical systems over others can sound VERY convincing while having little predictive value.
Based on those arguments the only thing that can be "worse" than an ideographic system would be a system where whole phrases are described with pictures.