What are the 'objective circumstances' that one young 'researcher' should take into account when choosing a 'research topic'?

Premise: I originally asked this on MathOverflow, but it was pointed out to me that it could be better fit for Academia Stack Exchange.

Note: I have received extremely varied advice on the following matter by various students slightly older than me, so I post the question here in the hope to get an objective 'technical take' from experienced researchers.

Assuming that there are several topics which are equally attractive to me and that the prospective advisors are all established researchers in their fields and "nice people", are there any objective circumstances that I should take into consideration when searching for a topic for an undergraduate research project to maximize my chances of making an "optimal choice"? Clearly, referring to research papers in mathematical education that partially support your remarks will be highly appreciated (although it is not necessary).

Additional remark: I guess that the natural generalization of this question to Ph.D. dissertation topics or general research advice is out of the scope of this website (although it is surely of some interest for several users and will be of interest for me in the following years).