People state that Romanian is closest in some aspects (grammar mainly), and that to learn a romance language studying latin may give you a leg up (which in my opinion just study the language), but for what language would this be uniquely bad for? For example, for which language has either the furthest grammar, vocabulary/cognate set, or has such a different sound set from Latin.
French or Portuguese have nasal vowels for an easy example; or some other criteria.
There is no definitive answer
This question is a very difficult one, since there is no clear way of measuring how much a language has changed. Also, some traces are kept by some and other traces by other languages, it means that some have been phonetically more conservative, while others, morphologically, syntactically etc. For instance, romanian has changed a lot phonectically speaking, more than italian did, but it retains a simplified version of latin's noun case inflections.
Asking a question like that is like asking which sibling looks more like their parents. One might say one of them have the hair that looks like her mother's, othe might say he has his dad's eyes, or even that she has the same personality as her father, but they all have different characteristics of their parents — none of them looks more like the other in a meaningful way. That's why you see so many different answers for this question, it is a matter of how do you analyse the languages to compare them. It also depends on which dialect of a certain language you're comparing.
EDIT: you said in your question that portuguese and french may be good candidates for least similar because of their nasal vowels, however, it is not a good argument because it is known that classical latin had nasal vowels as well, to make it even more complicated
French is a good candidate for the most evolved form of Latin. Very little has remained unchanged, and the situation would probably be worse if the French Académie had not relatinized French in the 17-18th centuries.
I have heard the claim that Spanish is the Romance language closest to Latin.
I have also heard the claim that Portuguese is the Romance language closest to Latin.
And I've heard that Romanian is the Romance language closest to Latin.
I've also heard that Italian is the Romance language closest to Latin.
And I've heard the same claim made about Romansh Ladin.
(I'd love to put all the linguists who made those claims together in a small room and make them come to some sort of agreement.)
Be aware that these are contradictory statements. Obviously, they can't be all correct -- but there could be some truth to all of them. (However, it does reinforce the saying that you shouldn't believe everything you read or hear -- even if what you hear comes straight from professional sources.)
Note that, from all the above statements, one language that's conspicuously absent is French. Does that mean French is the least similar to Latin?
To be fair, we can't discount the possibility that there is/was some variant of some Romance language that was even less similar to Latin, and has either died out, or is just not that well known.
There are also several French descendants (such as creole languages) that are farther from Latin. Do those count as Romance languages? Some people will say yes, some people will say no. It's not a clear-cut answer.
However, since there are no shortages of "This is the language closest to Latin" claims, and I've yet to hear one for French, makes me think that, well, French may be the best fit as an answer to your question -- barring any additional linguistic archaeology.
Gallo, Walloon and Gherdëina Ladin, or to generalise: the Oïl and Rhaeto-Romance languages, often heavily influenced by Celtic and Germanic, are the Romance lects furthest from Latin. Spanish, Aragonese, Italian, Sicilian, Sardinian, and Romanian (despite Slavic vocabulary) are closest to Latin.
