Hello sir! I am a community tutor and well here is what I know, the most common word order in English sentences is Subject-Verb-Object (SVO). and as an addition I can place this: Determiner, opinion, size, age, shape, color, origin, material and purpose! so Knowing these rules the way the sentence will be set up is the next one: "She is a popular successful singer." why? because popular is an opinion not a fact. since popular just apply for those who really like her but not the rest of humanity, so I would write that sentence this way: "She is a popular and successful singer." adding that little (and) so we can add two features! I am not an expert but I hope this may help you since I did it with all my good attitude.

Typically, your second choice would be taken to mean that she is a singer of "popular songs" - often shortened to "pop music" or "pop songs" - which is a genre or style of music. So, this indicated a successful singer in that style.- probably. Your first choice leaves open the style she sings in, but reports that she is both popular - people like her - and successful on some other criterion - perhaps she wins prizes or makes money. In the first choice, a comma after "popular" would be strongly preferred.